IN  MEMORIAM 
FLOR1AN  CAJORI 


STANiFORD'S 

PRACTICAL  ARITHMETIC, 

IN    WHICH 

THE  RULES  ARE  RENDERED  SIMPLE  IN  THE  OPERATION,  AND 
ILLUSTRATED  BY  A  VARIETY  OF 

USEFUL  QUESTIONS, 

CALCULATED  TO  GIVE  THE  PUPIL  A  FULL  KNOWLEDGE  OF 

FIGURES, 

IN  THEIR  APPLICATION  TO  TRADE  AND  BUSINESS  ; 
ADAPTED   PRINCIPALLY    TO 


DESIGNED  AS  AN  ASSISTANT  TO  THE  PRECEPTOR  IN  COMMUXt 
CATING,  AND  TO  THE  PUPIL  IN  ACQUIRING  THE 

SCIENCE  OF  ARITHMETIC  ; 

TO    WHICH   IS    ADDED, 

V  NEW  AND  CONCISE  SYSTEM  OF 

BOOK-KEEPING, 

BOTH   BY 

SINGLE  AND  DOUBLE  ENTRY  ; 
v  THE  FORMER 

CALCULATED  FOR  THE  USE  OF  TRADERS  IN  RETAIL.  BUSINE5Sl 
FARMERS  AND  MECHANICS  ; 

4^ 

AND   THE    LATTER 

'*  • 

FOR    WHOLESALE    DOMESTIC    AND    FOREIGN   TRADE,*AS    CON- 
DUCTED IN  THE 

UNITED  STATES. 


BY  DANIEL  STAMFORD,  A*  M. 

Author  of  the  Art  of  Reading  Jnd  the  Elements  of  English  Grammar. 

=, — ^     Tantum  scimus,  quantum  memoria  tenemus. 


BOSTON: 

PRINTED  BY  J.  H.  A.  FROST,  FOR  WEST,  RICHARDSON  &  LORD, 

No.  75,  CornhilJ, 

1818. 


DISTRICT  OF  MASSACHUSETTS—TO  WIT  : 

BE  it  remembered,  that  on  the  seventeenth  day  of  November,  in  tht 
year  of  our  Lord  one  thousand  eight  hundred  and  eighteen,  and 
in  the  forty-second  year  of  the  Independence  of  the  United  States  of 
America,  DANIEL  STANIFORD,  of  the  said  district,  has  deposited  in 
this  office,  the  title  of  a  book,  the  right  whereof  he  claims  as  author, 
in  the  words  following,  to  wit :  u  Staniford's  Practical  Arithmetic,  in 
44  which  the  rules  are  rendered  simple  in  the  operation,  and  illustrat- 
44  ed  by  a  variety  of  useful  questions,  calculated  to  give  the  pupil  a 
i4  full  knowledge  of  figures,  in  their  application  to  trade  and  business  ; 
44  adapted  principally  to  Federal  Currency  ;  designed  as  an  Assistant 
44  to  the  Preceptor  in  communicating,  and  to  the  pupil  in  acquiring 
44  the  science  of  Arithmetic  ;  to  which  is  added,  a  new  and  concise 
41  system  of  Book-Keeping,  both  by  single  and  double  entry  ;  the 
44  former  calculated  for  the  use  of  Traders  in  retail  business,  Farm- 
44  ers  and  Mechanics ;  and  the  latter  for  wholesale,  domestic  and 
*4  foreign  trade,  as  conducted  in  the  United  States.  The  whole  de- 
44  signed  for  the  use  of  Schools  and  Academies,  By  DANIEL,  STANI- 
44  FORD,  A.  M.  Author  of  the  Art  of  Reading,  and  Elements  of  Eng- 
*4  lish  Grammar." 

44  Tantum  scimus  quantum,  memoria  tenemus.'^ 

In  conformity  to  an  act  of  the  Congress  of  the  United  States,  en- 
titled, 4t  An  act  for  the  encouragement  of  learning,  by  securing  the 
copies  of  Maps,  Charts/and  Books,  to  the  authors  and  proprietors  of 
such  copies,  during  the  times  therein  mentioned  ;"  and  also  to  an 
act,  entitled,  u  An  act,  supplementary  to  an  act,  entitled  an  act,  for 
the  encouragement  of  learning,  by  securing  the  Copies  of  Maps, 
Charts,  and  Books,  to  the  authors  and  proprietors  of  such  Copies, 
during  the  times  therein  mentioned  ;  and  extending  the  benefits 
thereof  to  the  arts  of  designing,  engraving,  and  etching  historical  and 
other  prints." 

J.  W.  DAVIS, 
Clerk  of  the  District  of  Massachusetts. 

A  true  copy — Attest, 
J.  VV.  DAVIS,  Clerk. 


PREFACE. 


TO  the  question  commonly  asked,  on  the  appearance  of  a  new 
book,  "  Is  there  any  thing  new  in  it  ?"  the  author  replies,  that  al- 
though the  subject  of  arithmetic  can  admit  but  little  novelty,  yet  in 
this  treatise  there  is  something  new,  which  may  be  easily  discovered 
by  an  examination  of  its  contents. 

rhe_^eneral_rules_  in  jno£ti)JLljie_Arithmetics  used  in  our  schools 
are  too  synthetical  for  the  y_pung^Arithmelician.  They  contain  too 
many  principles  blended  together,  unaccompanied  with  sufficient 
elucidations.  The  scholar  therefore  is  in  danger  of  passing  over 
many  essential  parts,  without  fully  comprehending  them.  One 
design  therefore  of  this  treatise  is  to  give  an  Analysis  of  these  general 
rules,  resolving  them  into  their  simple  constituent  parts,  illustrating 
them  by  easy  practical  questions. 

As  the  work,  also,  is  principally  designed  to  furnish  a  system  of 
practical  Arithmetic,  adapted  to  the  currency  of  the  United  States, 
all  mathematical  demonstrations  ate-piirposely  omitted vto  give  place 
"  to  clear  illustrations  of  the  rules  by  easy  examples,  and  such  as  tend  j 
to  prepare  the  scholar  for  business ;  referring  those,  who  wish  to  ac- 
quire  a  knowledge  of  the  higher  branches  of  the  Mathematics  in 
those  elaborate,  though  useful  parts  of  the  science,  to  authors  par-  i 
ticularly  designed  for  the  purpose.  This  omission  will  leave  for  the  ; 
instructor  enough  for  the  exercise  of  his  skill  in  explaining  the  nature 
of  each  rule  to  the  pupil,  as  he  advances  in  his  pursuit,  and  becomes 
capable  of  comprehending  those  abstruse  parts  of  the  science.  The 
instructor  is  left,  also,  to  supply  at  his  discretion  various  additional 
questions  for  exercise  in  the  application  of  the  several  rules.  This 
will  prevent  the  fatal  practice,  too  much  indulged  among  scholars, 
of  copying  from  each  other's  manuscripts.  The  same  question  should 
never  be  proposed  by  the  instructor  a  second  time. 

Although  the  currency  of  the  United  States  is  generally  adopted 
through  the  work,  yet,  as  the  accounts  and  invoices  of  goods  of 
American  and  English  merchants  trading  together  are  kept  in  Sterling 
money,  so  much  only  of  that  money  is  applied  as  was  thought  neces- 
sary to  give  the  scholar  a  competent  knowledge  to  transact  that  part 
of  commercial  business. 

The  whole  arrangement  of  the  work  is  founded  on  the  natural  de- 
pendence of  the  several  parts  on  each  other  for  their  respective  ope- 
rations. A  few  remarks  are  offered  in  support  of  the  present  ar- 
rangement, 


iv  PREFACE. 

1.  REDUCTION.  As  by  this  rule  compound  addition,  multiplication 
and  division  are  performed,  its  place  naturally  precedes  them.     In 
reducing  time  365  days  is  commonly  called  a  year,  omitting  the 
fractional  parts. 

2.  VULGAR  FRACTIONS.     These,  having  their  origin  from  simple 
division,  seem  to  require  a  place  immediately  subsequent  to  that  rule  ; 
yet  as  their  operation  depends  on  other  rules,    a  place  is  assigned 
them,  following  those  on  which  they  are  dependent,  and  preceding 
others  which  depend  on  them  for  an  accurate  solution.     Vulgar  Frac- 
tions  being  indispensably  necessary  for  the  solution  of  many  impor- 
tant    questions   in   common   arithmetic    as   well    as   in   the    higher 
branches  of  Mathematics,  they  have  received  particular  attention 
in  this  treatise. 

3.  DECIMAL  FRACTIONS.    These  being  similar  in  their  operation 
with  whole  numbers,  seem  to  claim  a  place.  jn.jclojE£  connexion  with 
themj  yet  as  the  changing  of  them  from  one  form  into  another  is 
performed  by  other  rules,  their  order  should  succeed  them. 

4.  CIRCULATING  DECIMALS.    These  are  subjoined  for  the  benefit 
of  those  who  would  wish  to  have  a  comprehensive  view  of  the  whole 
nature  and  doctrine  of  Decimals  ;  particularly  for^  those  who  wish  to 
extend  their  mathematical  enquiries.     The  finite  decimals  are  con- 
tained in  the  first  cases,  and  are  all  that  is  necessary  for  common  bu- 
siness ;  the  circulates  may,  therefore.,  be  omitted  as  circumstances 
may  justify. 

5.  FEDERAL  MONET.    Some,  perhaps,  may  have  thought  it  more 
proper  to  arrange  this  currency  immediately  following  the  simple 
rules  of  Arithmetic,  because   of  their  simplicity;    yet  as  Federal 
jMQJftgyJs  fouttdedon,  the  nature  and  principles  of  Decimals,  and  per- 
formed by  the  same  rules  in  its  operation,  its  natural  order  is  cer- 
tainly subsequent  to  decimals.  Particular  attention  has  been  given  to 
it  in  connexion  with  decimals,  as  the  foundation  and  only  guide  for 
the  American  Accountant. 

6.  The  operations  of  Practice,  Tare  and  Tret,  with  Duodecimals, 
being  dependent  on  Compound  Multiplication   and   Division,   are 
placed  after  them. 

7.  RULE  or  THREE.  The  importance  and  extensive  utility  of  this 
rule  in  the  ordinary  concerns  of  life,  has  given  it  the  distinguishing 
title  of  "  The  golden  Rule."     As  most  of  the  subsequent  rules  in 
Arithmetic  are  performed  by  the  Rule  of  Three,  great  care  has  been, 
taken  to  render  it  intelligible  by  a  minute  investigation  of  its  nature, 
with  an  analysis  of  the  general  rule  in  simplifying  it  in  all  its  varieties. 

8.  Position,  Allegation  and  Permutation  are  inseited  at  the  close 
t>f  the  Practical  Arithmetic,  more  for  the  purpose  of  gratifying  curi- 
osity, than  for  their  utility  in  business. 


PREFACE.  v 

In  executing  the  work  nothing  superfluous  has  been  added,  and 
nothing  omitted  that  would  contribute  to  perfect  its  design,  and  ren- 
der it  serviceable  to  youth.  Those,  however,  who  are  in  the  habit 
of  teaching  superficially,  with  a  view  of  flattering  the  pupil  and  the 
parent  with  the  mistaken  idea  of  extraordinary  progress,  may  proba- 
bly raise  objections  against  the  work,  as_c^ntainingjtQfi.jnany.  things  _ 
to  be_committed  to  memory.  They  will  burden,  fatigue  and  confuse 
the  mind  of  the  scholar!  Such  persons  have  yet  to  learn  both  the 
susceptibility  and  capacity  of  the  young  mind,  and  that  although 
a  single  complex  idea  in  its  undigested  form,  crowded  into  the  mind 
of  a  child,  may  confuse  and  embarrass  it ;  yet,  in  direct  proportion 
to  the  number  of  simple  ones,  impressed,  will  it  become  more  invigo- 
rated, more  enlightened,  more  improved.  Similar  objections  would 
as  readily  be  started  against  an  abridgement  of  the  smallest  size,  by 
those  only  who  have  neither  the  ability  nor  inclination  to  lay  the 
whole  nature  of  the  subject  open  to  the  understanding,  and  lead  the 
pupil,  gradually,  into  that  train  of  logical  reasoning,  peculiar  to  the 
mathematics. 

I     9.  BOOK-KEEPING.  This  useful  branch  of  learning  has  been  almost  i  L 
totally  neglected  in  our  schools  and  academies.     The  neglect  of  a  / 
study  so  essential  to  the  best  literary  interest  of  youth  proves  a  nia-^j/ 
terlal  defect  in  the  present  system  of  education.     It  may,  perhaps, 
be  attributable,  in  a  great  degree,  to  the  want  of  a  concise  treatise 
on  the  subject,  divested  of  those  numerous  difficulties  which  envelope 
in  mystery  even  the  best  system  extant.     So  intricate  and  tedious  are 
they,  for  the  most  part,  that  even  instructors  themselves  have  been 
deterred  from  giving  instruction  by  them. 

The  short  system  in  this  publication  has  been  used  by  the  author 
with  considerable  success.  It  is  now  offered  as  an  attempt  to  simplify 
the  Art  of  Book-keeping,  and  to  adapt  it  to  the  capacity  of  youth. 
Jt  furnishes  such  rules  and  explanatory  remarks  in  discriminating  the 
titles  of  Dr.  and  Cr.  in  journalizing  and  posting  the  several  mercan- 
tile transactions,  as  were  thought  best  calculated  to  render  easy  and 
clear  a  subject  of  so  much  importance. 

Of  such  immense  benefit  is  this  part  of  science  to  a  young  man  of 
any  respectable  standing  in  society,  that  no  scholar  should  be  per- 
mitted to  leave  school,  to  become  an  apprentice  either  to  a  merchant, 
a  mechanic,   or  even  to  a  farmer,  without  a  thorough  knowledge  of 
the  principles  and  forms  of  Book-keeping ;  as  on  his  knowledge  of      1/1 
jhis_a£t  essentially  depends  the  security  of  all  the  fruits  pOiis  iTUJus__  jf  I 
try  through  life.     Many  mechanics  and  farmers  have  lost  half  their  ^/ 
earnings  by  neglecting  to  make  a  regular  entry  of  their  daily  trans- 
actions peculiar  to  their  employment ;  and  even  wealthy  merchant? 


vi  PREFACE. 

have  become  the  melancholy  objects  of  penury  and  distress  through 
the  same  neglect. 

The  best  interest  of  youth  would  be  essentially  promoted,  were 
this  important  branch  of  science  introduced  into  our  schools,  and  to 
constitute  a  prominent  part  of  their  education. 

The  work,  with  its  trifling  errors,  is  now  presented  to  the  public  in 
full  confidence  that  it  will  meet  the  acceptance  it  deserves.  It  claims 
no  preference  to  the  numerous  publications  on  this  subject.  The 
author  asks  that  patronage  only,  to  which  it  is  entitled  by  its  real 
merits.  And  if,  kind  reader,  you  can  find  a  better  treatise,  freely 
adopt  it ;  u  At  si  non  rectius  invenire  potes,  hoc  utere  mecum  ;'* 
And  in  either  case  it  will  be  perfectly  satisfactory  to 

THE  AUTHOR. 

Roston,  September  30,  1818, 


The  following  typographical  errors  have  escaped  timely  attention,  which  the  reader 
is  respectfully  requested  to  correct  on  the  margin  of  the  page  referred  to  in  th*  table  of 

ERRATA. 
Page 

16— Exam.  7,  multiplicand,  for  84  read  48. 
20— Exam.  9,  dividend,  for  467  read  464. 
26 — Dry  measure,  for  4  gals,  read  2  gals. 
29 — Question  18,  insert  2  yds. 
30— Exam.  30,  after  37-^-,  insert  1S=. 

33— Question  13,  insert  cwt.  after  9  1-2,  also,  Ib.  after  31920. 
33 —  15,  Ans.  for  drs.  read  oz. 

40 — Exam.  11,  Long  measure,  subtrahend,  for  2  yds.  read  4  yds. 
43 — Exam.  12,  Time,  in  Ans.  for  3  weeks  read  0. 

G3 — Note  first,  for  numerator  read  denominator,  and  for  denom.  read  numerator, 
64 — Question  6,  for  divided  read  multiplied. 
67 — Case  II,  line  4,  for  left  read  right. 
67 — Exam.  4,  dele  the  second  2. 
80 — Exam.  12,  in  quotient,  for  75  read  25. 
109 — Exam.  26,  for  14<£.  read  4d. 
114— Question  5,  in  Ans.  for  £6,6  2-3  read  85,5  5-9. 
117 — Exam.  13,  Ans.  for  59  urals.  read  62  gals. 
156 — Line  7th  from  top,  for  00  read  700. 
172 — Line  9th  from  bottom,  dele  0  in  dividend. 
181  and  182,  for  proportion  read  proposition. 

256— Personal  accounts,  first  line,  for  Dr.  read  Cr.  also  in  lecond  line,  for  Cr,  read  DJ  , 
290— Dr.  Sugar,  for  589  read  549, 
4— Preface,  remark  S,  for  timpHcity  read  tlmilarity.  ~* 
40 — Exam.  10,  for  tcru.  grt.  read  dn,  tcru. 
48 — Exam.  4,  Ans.  for  1-2  read  1-4. 
58— Case  IX.  for  denominator  read  numerator, 
78— -Exam.  2,  dele  0  in  dividend,  also  7  in  quotient. 
96— Second  method,  top  line,  in  dollars  insert  8. 

167— Exchange,  France,  for  4  6rf.  sterl.  exchange  at  par.  read  2  6d,  sterliim- 
193— ABS.  4,  decimal,  dele  second  3. 


RECOMMENDATIONS. 

Boston,  October  Qth,  1818. 

AT  the  Annual  Meeting  of  the  u  ASSOCIATED  INSTRUCTERS  OF 
YOUTH  IN  THE  TOWN  OF  BOSTON  AND  ELSEWHERE,"  the  following 
Report  of  a  Committee  was  made  and  accepted,  viz  : 

u  The  Committee  appointed  by  the  Association  to  examine  a 
Treatise,  entitled,  '  Practical  Arithmetic,  and  a  short  System  of 
Book-keeping,'  by  DANIEL  STANIFORD,  A.  M.  have  attended  to 
that  service,  and  after  a  careful  examination,  are  of  opinion,  that  it 
is  a  work,  better  calculated  to  facilitate  the  progress  of  youth,  in 
these  useful  and  important  sciences,  than  any  treatise  of  the  kind,  of 
which  we  have  any  knowledge. 

Signed,  JONA.  SNELLING,  ) 

J.  R.  COTTING,       >  Committee. 
BENJAMIN  HOLT,  $ 
A  true  copy  from  the  records  and  files  of  the  Association. 

Attest,  THOS.  PAYSON,  Sec.  A.  I.  Y. 

THE  undersigned  having  attentively  examined  a  treatise  on  u  Book- 
keeping,11 By  Daniel  Staniford,  A.  M.  are  of  opinion  that  it  is  better 
calculated  to  give  pupils  a  knowledge  of  the  rudiments  of  this  impor- 
tant science,  then  any  one  of  the  kind  we  have  hitherto  seen. 

The  introduction  contains  a  large  number  of  valuable  rules  for 
journalizing  and  posting,  which  are  too  often  omitted  in  treatises  of 
this  kind  ;  and  the  several  accounts  in  the  Waste-book  are  so  judi- 
ciously arranged  as  examples  to  each  rule,  that  they  may  be  readily 
comprehended  by  the  learner.  We  sincerely  hope  that  it  will  have 
a  general  circulation  in  our  schools  and  academies, 

J.  COTTING, 
EDWARD  JEWETT. 


Explanation  of  the  Characters  used  in  the  following  Work. 

=      Equal.     The  sign  of  equality  ;  as  4  qrs.  =1  cwt. 

-{-       Plus,  or  more.     The  sign  of  Addition  ;  as  8-f-4=12. 

—       Minus,  or  less.     The  sign  of  Subtraction  ;  as  6 — 4=2. 

X       Multiplied  by.     The  sign  of  Multiplication  ;    4X3=12. 

Letters  joined  like  a  word  express  the  continual  multiplicatio* 
of  them  as,  apr=aXpXr- 

-r-       Divided  by.     The  sign  of  Division  ;  as,  12-f-4=3. 

Division  is  likewise  expressed  by  numbers  placed  in  the  form  of  a 
fraction  ;  as  2_7  =9.  Letters  also  placed  in  the  form  of  a  frac- 
tion signify  that  the  upper  letters  are  to  be  divided  by  the  lower. 

:     :  :     :     The  sign  of  Proportion  ;  as  4  :  8  :  :  12  :  24,  that  is,  as  4 
is  to  8,  so  is  12  to  24. 

•")  2 ,  or  32 ,      Signifies  the  second  power,  o*  square. 

•H  3,  or  43,      Signifies  the  third  power,  or  cube. 

^/         Signifies  the  square  root. 

%*/       Signifies  the  cube  root. 

JVote.    The  number  belonging  to  the  above  ligas  of  powers,  and  roots,  is  called  the 
index  or  exponent. 

A  line  or  vinculum,  drawn  over  several  numbers,  signifies,  that  the 
numbers  under  it  are  to  be  considered  jointly  ;  as  8 — 3-j-4=l  ; 
but  without  the  line,  8— 3-{-4=9. 


CONTENTS. 

Page 

Numeration, 10 

Simple  Addition,     ....  12 

Subtraction, , 13 

Multiplication, 14 

Division, 17 

ables  of  coins,  weights  and  measures, 22 

Reduction, 26 

Compound  Addition, 36 

Subtraction, 39 

Multiplication, 41 

Division, 46 

-"Vulgar  Fractions, •     .      51 

Decimals,  finite  and  circulating, 64 

Federal  Money, 87 

Practice,     .     .     , 104 

Tare  and  Tret, 109 

Duodecimals,  or  Cross  Multiplication, 113 

Single  Rule  of  Three, 121 

Double  Rule  of  Three, 131 

Fellowship  Single, 133 

Double, 135 

Simple  Interest  in  Federal  Money, 136 

Sterling  Money, 145 

Commission, 147 

Buying  and  Selling  Stocks, 147 

Ensurance, 148 

Compound  Interest, 150 

Discount, .      152 

Bank  Discount, 153 

Equation  of  Payments, 154 

Barter, 154 

Loss  and  Gain, 157 

Exchange, 159 

Conjoined  Proportion, 172 

Arbitration  of  Exchanges, 173 

Ivolution, 174 

Evolution, 175 

Square  Root, 176 

Cube  Root, 178 

Biquadrate  Root, 179 

Arithmetical  Progression, 181 

Geometrical  Progression, .      .      .      183 

Permutation,     . .      .      189 

Simple  Interest  by  decimals, 191 

Compound  Interest  by  decimals, 194 

Book-Keeping  by  Single  Entry, 198 

Double  Entry, 236 

Appendix, 318 

Mercantile  Forms, 320 


PRACTICAL  ARITHMETIC. 


ARITHMETIC  is  the  art  of  computing  by  numbers. 

Number  is  that  which  answers  directly  to  the  question, 
"  How  many  ?"  and  is  either  an  unit,  a  multitude  of  units, 
part  or  parts  of  an  unit,  or  a  mixt  expression. 

The  whole  art  of  Arithmetic  is  comprehended  in  the 
Tarious  operations  of  the  five  following  rules,  viz. 

1.  Numeration,  or  Notation. 

2.  Addition. 

3.  Subtraction. 

4.  Multiplication. 

5.  Division. 

Practical  Arithmetic  is  the  application  of  the  preceding 
fundamental  rules,  so  as  to  be  most  useful  in  business. 

NUMERATION. 

NUMERATION  teaches  to  read,  or  write,  any  number. 

All  numbers  are  expressed  by  ten  characters,  called  fig- 
ures, or  digits,  viz.  1,  2,  3,  4,  5,  6,  7,  8,  9,  0.  The  nine 
first  are  called  significant  figures  5  the  last,  a  cipher,  or 
nought. 

The  cipher  is  of  no  value  when  it  stands  alone,  or  at 
the  left  hand  of  a  whole  number ;  .but,  when  annexed  to  any 
significant  figure,  it  increases  its  value  ten-fold. 


£0  NUMERATION. 

The  simple  value  of  any  figure  may  be  known  by  inspec- 
tion, and  the  following  table  plainly  shows  the  local  value 
of  any  figure  from  the  place  of  units  towards  the  left  hand, 
as  far  as  may  answer  every  purpose  of  calculation. 

NUMERATION  TABLE 


CO                      &*                      i-< 

9 

8  7 

.  6 

5 

4 

.  3 

2 

1 

9 

0  0 

.  0 

0 

0 

.  0 

0 

0 

8  0 

.  0 

0 

0 

.  0 

0 

0 

7 

.  0 

0 

0 

.  o 

0 

0 

6 

0 

0 

.  0 

0 

0 

5 

0 

.   0 

0 

0 

4 

.  0 

0 

0 

3 

0 

0 

2 

0 

1 

RULE.  There  are  three  periods ;  the  first  on  the  right 
hand,  Units;  the  second  Thousands;  and  the  third  Mil- 
lions, each  of  which  consists  of  three  places  or  figures. 
Reckon  the  third  figure  of  each  period,  from  ihe  left  hand, 
so  many  Hundreds,  the  next  Tens,  and  the  other,  so  many 
Units,  of  what  is  written  over  them;  as  the  first  period  on 
the  left  hand,  read  thus,  Nine  hundred  eighty-seven  mil- 
lions }  the  second  period,  Six  hundred  fifty-four  thousands; 
and  the  other  period,  Three  hundred  and  twenty  one  units. 

It  is  obvious,  that  numbers  increase  in  a  ten-fold  propor- 
tion from  the  right  hand  towards  the  left:  that  is,  any 


NUMERATION.  ^ 

figure,  in  the  place  of  teas,  is  ten  times  the  value  of  the 
same  figure  in  the  place  of  units ;  and  any  figure  in  the 
place  of  hundreds,  is  ten  times  the  value  of  the  same  figure 
io  the  place  of  tens,  &c. 

CASE  I. 
To  read  any  number. 

RULE.  Find  out  the  place  of  each  figure  by  the  Table, 
and  to  the  simple  value  of  each  figure  join  the  name  of  its 
place,  beginning  at  the  left  hand,  and  reading  towards  the 
right. 

EXAMPLES. 
Read  the  following  numbers. 

21 

321 

4321 

54321 

654321 

7B54321 

87654321 

.  987654321 

CASE  II. 
To  write,  any  number  in  figures. 

RULE.  AVrite  down  ciphers  to  as  many  periods,  qr 
places,  as  are  named  in  the  given  number ;  then,  beginning 
at  the  left  hand,  observe,  at  each  place,  what  significant 
figure  is  named,  and,  taking  away  the  cipher,  write  tlie 
significant  figure  in  its  place. 

EXAMPLES. 

Write  in  figures  the  following  : — 
Five  hundred  and  twenty-four. 
Nine  thousand,  seven  hundred  and  ten. 
One  hundred  millions,  one  hundred  thousand,  and  ten. 
One  hundred  millions  and  one. 


SIMPLE  ADDITION. 


II.*    .   .    . 

.  Two. 

III.  .    .   . 

.     Three. 

iv.t    .   .   . 

.  Four. 

V.      ... 

.     Five. 

VI*     .    .    . 

.  Six. 

VII.  .     .     . 

.     Seven. 

VIII.   .     .     . 

.  Eight. 

IX.    ... 

x  

Ten. 

XL 

Eleven, 

JVtymeration  by  Roman  Letters. 

XXX Thirty. 

XL Forty. 

L Fifty. 

LX Sixty. 

LXX.       .     .     .  Seventy. 

LXXX.      .     .     .  Eighty. 

XC Ninety. 

C,  .  Hundred. 


XII Twelve. 

XIII.      .     .     .     Thirteen. 

XIV Fourteen. 

XV Fifteen. 

XVI Sixteen. 

XVII.  .  .  .  Seventeen. 
XVIIL  .  .  .  Eighteen. 
XIX.  .  .  .  Nineteen. 
XX Twenty. 


CC.  . 

ccc. 
cccc. . 

D.  .  .  . 
DC.  . 
DCC.  . 
DCCC. 
DCCCC. 

M 

MDCCCXVIII. 

Eighteen  hundred 

eighteen. 


Two  Hundred. 
Three  Hundred. 
Four  Hundred. 
Five  Hundred. 
Six  Hundred. 
Seven  Hundred. 
Eight  Hundred. 
Nine  Hundred. 
.  .  Thousand. 


and 


SIMPLE  ADDITION. 


ADDITION  is  the  collecting  of  several  numbers  of  the 
same  denomination  into  one  sum. 

RULE.  Place  the  numbers  under  each  other  according  to 
the  value  of  their  places,  by  putting  units  under  units,  tens 
Under  tens,  &c. ;  then,  beginning  at  the  right  hand  column, 
add  the  figures  in  it,  and  set  down  the  units,  and  carry  the 
tens  to  the  next  left  hand  column,  continuing  so  to  do  to  the 
last  column,  under  which  set  down  its  whole  amount. 

The  total  amount  in  addition  is  called  the  sum. 

PROOF.  Add  the  figures  downwards  in  the  same  manner 
as  they  were  added  upwards,  and  the  sum  will  be  the  same. 

*  As  often  as  any  character  is  repeated,  so  many  times  its  value 
is  repeated. 

t  A  less  character  before  a  greater  diminishes  its  value, 
i  A  less  character  after  a  greater  increases  its  value. 


SIMPLE  SUBTRACTION.  13 

EXAMPLES. 

4874835          8433487 
7367485  4783438 

4363567  4365687 

8934874  8749863 


25540761          26332475 


SIMPLE  SUBTRACTION. 

SUBTRACTION  leaches  to  find  the  difference  between  two 
numbers  of  the  same  denomination. 
It  has  three  parts,  viz. 

1.  The  greater  number,  or  the  minuend. 

2.  The  less  number,  or  the  subtrahend. 

3.  The  difference,  or  remainder. 

RULE.     1.  Place  the  less  number  under  the  greater,  ac- 
cording to  their  value,  as  in  addition. 

2.  Beginning  at  the  right  hand,  subtract  each  under  figure, 
from  that  which  stands  above  it,  setting  the  remainder  un- 
der them,  and  the  several  remainders  together  will  express 
the  difference  required. 

3.  If  the  under  figure  is  greater  than  that  above  it,  ber- 
row  ten  and  add  it  to  the  upper  figure,  from  which  sum 
take  the  under  figure,  setting  down  the  remainder  as  be- 
fore; remembering,  that  every  time  ten  is  borrowed,  to 
earry  one  to  the  next  under  figure,  before  it  is  subtracted. 

PROOF.     Add  the  difference  to  the  less  number,  and  their 
sam  will  be  equal  to  the  greater.  _ 

EXAMPLES. 

8734874       Minuend.       83010014  834874 

4837841       Subtrahend.       378749  18700 

*  3897033       Difference.     82631265  816174 


8734874       Proof. 

QUESTIONS. 


1.  If  I  lend  my  friend  $9480  and  receive  in  part  pay- 
ment 81987;  how  much  remains  due  ?  Ans-  S7493. 

2.  The  revolutionary  war  in  America  commenced  with 
Great  Britain,  in  the  year  1775,  (April  19);  how  many  years 
since,  the  present  year  being  1818  ?  Ans.  43  yearsr. 

8* 


14,  SIMPLE  MULTIPLICATION. 

3.  Peace  between  the  United  States  and  Great  Britain 
took  place  in  1733,  and  war  again  declared  in  1812;  how 
long  did  the  peace  continue  ?  ^  Ans.  29  years. 


SIMPLE  MULTIPLICATION. 

SIMPLE  MULTIPLICATION  is  a  short  method  of  performing 
many  additions. 
It  has  three  parts,  v'iz. 

1.  The  Multiplicand,  or  sum  multiplied. 

2.  The  Multiplier,  or  sum  multiplied  by. 

3.  The  Product,  or  number  found  by  the  operation. 
NOTE.     The  Multiplicand  and  Multiplier  are  called  the  factors. 

MULTIPLICATION  J1ND  DIVISION  TABLE. 


2  Times 

2|are   4 

4  Times 

4  are  16 

7  Times 

7  are 

49 

3 

6 

5 

20 

8 

56 

4 

8 

6 

24 

9 

63 

5 

10 

7 

20 

10 

70 

6 

12  1- 

8 

32 

11 

77 

1 

14 

9 

36 

12| 

84 

8 

16; 

10 

40 

8  Times 

~8;aTe* 

64 

9 

18; 

11 

44 

9 

72 

10 

20  1 

12 

48 

10 

80 

11 

22  5  Times 

5  are  25 

11 

88 

12 

24 

6 

30 

12 

96 

3  Times 

3 

are 

9 

7 
8 

35 

40 

9  Times 

9 
10 

are 

81 

90 

f 

4 

12 

9 

J45 

11 

99 

5 

15 

10 

50 

12 

108 

6 

18 

11 

55 

7 

21 

12 

60 

lOTimes 

10  are 

100 

8 

24  6  Times 

6  are  36 

11 

110 

9 

27 

7 

42 

12 

120 

10 

30 

3 

Aft 

11 

33 

9 

rO 

54 

1  1  Times 

11 

are 

121 

1* 

36 

10 

60 

12 

132 

11 

66 



— 

— 

—  _ 

| 

12 

72  12  Times 

12 

are 

144 

NOTE.  The  pupil  should  be  instructed  to  change  the  multiplier  in 
the  preceding  table.  Example — 6  tii»es  8,  or  8  times  6,  are  48,  and  so  for 
the  rest. 


SIMPLE  MULTIPLICATION. 


15 


GENERAL  RULE. 

1.  Place  the  multiplier  under  the  multiplicand  according 
to  the  value  of  the  figures,  as  in  addition. 

2.  Beginning  at  the  right  hand,  multiply  each  figure  in 
the  multiplicand  by  each  in  the  multiplier,  placing  the  first 
figure  of  every  line  directly  under  its  respective  multiplier, 
and  to  the  product  of  the  next  figure  carry  one  for  every 
ten,  as  in  addition. 

3.  Add  the  several  products  together,  and  their  sum 
will  be  the  total  product  required. 

PROOF.  Make  the  multiplicand  the  multiplier  and  the 

multiplier  the  multiplicand,  and  proceed  as  before  in  the 

operation,  if  the  product  is  like  the  former  the  work  is 
right. 

CASE  I. 

When  the  multiplier  is  not  more  than  12. 
RULE.     Multiply  the  given  number  by  the  whole  multi- 
plier. 


1. 

87487487 
8 

699899896 

3. 

7009748 
11 

77107228 


EXAMPLES. 

Multiplicand. 
Multiplier. 

Product. 


4387936 
9 

39491424 


521984952 


CASE  II. 


AVhen  the  multiplier  is  more  than  12,  and  such  as  two 
or  more  numbers  in  the  table,  when  multiplied  together, 
will  make  it. 

RULE.  Multiply  the  given  number  by  one  of  these  fig- 
ures, and  the  product  by  the  other:  the  last  product  will 
be  the  answer. 


SIMPLE  MULTIPLICATION. 

EXAMPLES. 

5.  6. 

Multiply     389074   by  24.  3350746    by  48. 

4X6=24.  4  6    6X8=4*. 


1556296  50104476 

6  8 


9337776  400835808 


CASE  III. 

When  the  multiplier  consists  of  several  figures. 
RULE.     Multiply  each  figure  in  the  multiplicand  as  di- 
rected in  the  general  rule. 

EXAMPLES. 

7.  8. 

847483567  749084 

768  759 


3899868536  6741756 

2924901402  3745420 

3412384969  5243588 


374387379456         568554756 


CASE  IV. 

When  there  are  ciphers  either  in  the  multiplicand  or  mul- 
tiplier, or  in  both. 

RULE.  Omit  the  ciphers  and  multiply  by  the  significant 
figures,  as  before  directed  5  and  to  the  product  annex  as 
many  ciphers  as  are  given  in  both  the  factors. 

EXAMPLES. 

9.            10.  11. 

87487487      8740084500  98736509 

120            11  900 


10498498440     96140929500   88862850000 


SIMPLE  DIVISION.  ^ 

CASE  V. 

When  there  are  ciphers  between  the  significant  figures 
of  the  multiplier. 

RULE.  Omit  them  in  the  operation,  and  multiply  by  the 
significant  figures,  placing  the  first  figure  of  each  product 
tinder  its  respective  multiplier. 

EXAMPLES. 

12.  13. 

48748043  48748744 

40007  9003 


341236301  146246232 

194992172  438738696 


1950262S56301         438884942232 


CASE  VI. 

To  multiply  by  10,  100,  1000,  &c. 
RULE.     To  the  given  number  annex  as  many  ciphers  as 
there  are  iu  the  multiplier. 

EXAMPLES. 

Multiply  78  by  10,  100,  and  1000.    CTo  multiply  by  parts, 
Product.  780  ....  7800  .  .  78000.  \  see  Division  Case  VII. 


SIMPLE  DIVISION. 

SIMPLE  DIVISION  shows  how  often  one  number  is  contain- 
ed in  another,  of  the  same  denomination. 

It  has  four  parts ;  viz. 

1.  The  Dividend,  or  sum  divided. 

2.  The  Divisor,  or  sum  divided  by. 

3.  The  Quotient,  or  answer. 

4.  The  Remainder,  or  what  is  left  after  division. 

The  remainder  is  of  the  same  name  with  tfie  dividend 
and  quotient,  and  must  always  be  less  than  the  divisor. 


£g  SIMPLE  DIVISION. 

PROOF.  Multiply  the  quotient  by  the  divisor,  add 
the  remainder,  if  any,  to  the  product,  and  the  sum  wiH 
he  equal  to  the  dividend. 

CASE  I. 

When  the  divisor  is  not  more  than  12,  it  is  called  Short 
Division  5  then  the  quotient  is  placed  under  the  dividend. 

RULE.  1.  Find  how  often  the  divisor  is  contained  in  the 
first  figure,  or  figures  of  the  dividend,  setting  it  under  the 
dividend,  and  carrying  the  remainder,  if  any,  to  the  next 
figure,  as  so  many  tens. 

2.  Find  how  often  the  divisor  is  contained  in  this  divi- 
dend, and  set  it  down  as  before,  continuing  so  to  do,  till  all 
the  figures  in  the  dividend  are  used. 

NOTE.  The  work  in  Short  Division  is  done  mentally,  that  is,  divided 
in  the  mind,  and  the  result  only  written  down;  whereas  in  Long  Di- 
vision the  operation  is  written  at  large. 

EXAMPLES. 

1.  9. 

Divisor.     8)38748747  9)876874854 


-Rem. 


Quotient.        4843593 — 3  97430539--.3 

8  -* , 

Proof.  38748747 


NOTE.  When  there  is  no  remainder,  the  quotient  is  the  perfect  an- 
swer to  the  question ;  but  if  there  is  a  remainder,  set  it  at  the  end  of 
the  quotient,  above  a  small  line  with  the  divisor  under  it,  which  is  part 
of  another  unit.  Hence  the  origin  of  Vulgar  Fractions,  the  remainder 
being  the  numerator,  and  the  divisor  the  denominator,  which  will  Ire 
particularly  explained  in  their  proper  place. 

3.  4. 

11)7387487487  12)87487487 


671589771-6  rem.  7290623-11  rem. 

CASE  II. 

Long  Division  is  when  the  divisor  exceeds  12,  then  the 
quotient  must  be  placed  at  the  right  hand  of  the  dividend. 

RULE.  1.  Having  written  the  divisor  at  the  left  hand  of 
the  dividend,  find  how  many  times  the  divisor  is  contained 


SIMPLE  DIVISION. 


19 


in  the  first  figure  of  the  dividend,  or  if  not  in  the  j?rs£,  how 
many  times  it  is  contained  in  the  two  first  figures,  and  place 
the  number  at  the  right  hand  of  the  dividend  for  the  quo- 
tient figure. 

2.  Multiply  the  divisor  by  the  quotient  figure,  and  place 
the  product  under  the  dividend. 

3.  Subtract  this   product  from  the  dividend,  and  to  the 
remainder  bring  down  the  next  figure  in  the  dividend,  and 
write  in  the  quotient  the  number  of  times  the  divisor  is  con- 
tained in  this  new  dividend. 

4.  Multiply  the  divuor  by  the  last  quotient  figure  and 
proceed   as  before  directed  ;  thus  continue  to  do  till  all  the 
figures  in  the  dividend  are  brought  down. 

If  the  remainder,  after  having  bro  flown  a  figure,  is 
still  less  than  the  divisor,  a  cipher  in  »:  be  carried  to  the 
quotient,  and  another  figure  brought  dovni,  and  wrought  as 
before  directed. 

EXAMPLES. 

5.  6. 

Divisor.     Dividend.     Quotient. 

24)34748748(1447864^          48)74848748(1 559348 j| 

24  48 

J07  288 

96  240 

.114  284 

96  240 

188  418 

163  432 


207  167 

192  144 

154  234 

144  192 

108  428 

96  301 

12  Remainder.  44  Remainder. 

NOTE.     The  fraction  must  always  be  reduced  to  its  lowest  terms 
before  it  i*  annexed  to  the  quotient,  as  in  the  two  last  Examples. 


£0  SIMPLE  DIVISION, 

CASE  III. 

When  the  divisor  is  a  composite  number,  that  is,  such  an 
two  or  more  figures  in  the  table,  when  multiplied  together,; 
will  make  it. 

RULE.  Divide  the  dividend  by  one  of  these  figures,  and 
the  quotient  by  the  other ;  the  last  quotient  will  be  the  an- 
swer. 

EXAMPLES. 

7.  8. 

Divide  84874  by  48.  Divide  487488  by  84. 

6X8=48.  7X12=84. 

6)84874  7)487488 

8)14145-4  1st  rem.  12)  69641-1  1st  re. 

1768-1  2d  rem.  5803-5  2drem. 

NOTE.  To  find  the  true  remainder,  when  there  is  a  remainder  to 
each  of  the  quotients. 

RULE.  Multiply  the  first  divisor  into  the  last  remainder, 
to  the  product  add  the  first  remainder,  the  sum  will  be  the 
true  remainder. 

Thus  in  example  7.  The  first  divisor  6x1  the  last  re- 
mainder is  6,  to  which  add  4  the  first  remainder,  the  sum  is 
10  equal  to  the  true  remainder. 

CASE  IV. 

When  there  are  ciphers  in  the  divisor. 
R\JLE.  Cut  them  off,  and  as  many  places  from  the  right 
liand  of  the  dividend ;  but  they  must  be  annexed  to  the 
remainder. 

EXAMPLES. 

9.  10. 

42,000)467567,000  11,00)435678,34 


38713—11000  Rem.  39607—134  Rem. 

CASE  V. 

To  divide  by  10,  100,  1000,  &c. 

RULE.  Cut  off  as  many  places  from  the  right  hand  of 
the  dividend,  as  there  are  ciphers  in  the  divisor,  the  left 
Land  figures  will  be  the  quotient,  and  the  right  hand  figures 
cut  off  will  be  the  remainder. 


SIMPLE  DIVISION.  21 

EXAMPLES. 

11.  Divide     787484  by  10.    .     .  Answer,  78748T% 

12.  ...      787104  by    100.  .     .  Answer,  7874^ 

13.  ...     787484  by  1000.     .  Answer,     787TWo 

CASE  VI. 
To  divide  by  fractions,  or  parts  of  an  unit. 

RULE.  If  the  numerator,  or  upper  figure,  is  an  unit, 
multiply  the  given  number  by  the  denominator,  or  un- 
der figure,  and  the  product  will  be  the  answer:  but  if  the 
numerator  is  more  than  an  unit,  multiply  the  given  num- 
her  by  the  denominator,  and  divide  the  product  by  the  nu- 
merator. 

EXAMPLES. 

14.  Divide  848  by  j.  16.  Divide  484  by  i. 

4=denominator.  2=deuomina. 


3392  Answer.  968  Answer. 

15.  Divide  483  by  f .  17.  Divide  496  by  f. 

4=denominator.  8=denomina. 


>Tumer.  3)1932  Numer.  3)3968 

644  Answer.  1322f  Answer. 

CASE  VII. 

To  multiply  by  fractions,  or  parts  of  an  unit. 

RULE.  If  the  numerator  is  an  unit,  divide  the  given 
number  by  the  denominator,  and  the  quotient  will  be  the 
answer;  but  if  the  numerator  exceeds  an  unit,  multiply 
the  given  number  by  the  numerator,  and  divide  the  product 
by  the  denominator,  the  quotient  will  be  the  answer. 

EXAMPLES. 

18.  Multiply  843  by  1.          19.  Multiply  874  hy  |. 
Deaomin.  4)843  Denomin.  2)874 

210|  Ans.  437  Ans. 

3 


COINS,  WEIGHTS,  AND  MEASURES. 


20.  Multiply  8740  by  f .          21.  Multiply  840  by  f . 
3=Numerat. 


Denom.  4)26220 

6555  Ans. 


5=Numerat. 
Denom.  3;4200 

525  Ans. 


TABLES  OF  COINS,  WEIGHTS,  AND  MEASURES. 
1.  ENGLISH  MONEY. 

4  Farthings,   marked  qis.    make    1  Penny,   marked    d. 

12  Pence        1   Shilling,     .     .      s. 

20  Shillings        .......      1  Pound,  .     .     .    £. 

NOTE.  4d=l  groat. 

PENCE  TABLE. 


to 


Pence.                  s.  d. 

Shillings. 

20  equal  to    1     8 

2     equal 

30    ...     2    6 

3     .     . 

40    ...     3    4 

4     .     . 

60    ...     4    2 

5     .     . 

60    ...     5    0 

6     .     . 

70    .      .     .     5  10 

7     .     . 

80    ...     6     8 

8     .     . 

90    ...     7     6 

9     .     . 

100    ...     8     4 

10     .     . 

110    ...     9     2 

11      .     . 

120    .     .     .  10    0 

12     .     . 

d. 

24 
36 

Shillings.             £.  s. 
20  equal  to  1 
30     ...    1    10 

48 

40 

...    2 

60 

50 

.     .     .    2  10 

72 

60 

...    3 

84 

70 

...   3   10 

96 

80 

...    4 

108 

90 

...    4   10 

120 

100 

...    5 

132 

HO 

...   5  10 

.  141   120     ...    6 


COMPARATIVE    VALUE    OF    COINS. 


Lawful.  Sterl.  Fed.  Mon. 
A  Guinea  =£1    8=£l    1=$4  66  2-3 
Doubloon  =   4    8=    3    6=14662-3 
Johanna    =    2    8=    1  16=    8 
Dou.Joh.=    416=    312=16 
Moidore    =    1  16=    1    7=    6 
Pistole       =    1    2=    0  16.6=3  77  1-3 
Crown       =    0    6.8=0    5=    1   10 
Spanish  doll.    0    6=         4.6=1 
Engl.  shil.=         1.4=      1=        222-9 
French  Frank  1.1$  —  181-2 

Pagoda  of  China=$l  94 
Tale  of  China   =    1  40 
Milrea  of  Portu.=   1  25 
Livre  Tournois  =        18  \-:l 
Rixdol.  of  Den.=    1 
Guilder  or  Florin=       40 
Ruble  of  Russia=       66 
Rupee  of  Bengal=       55  1-2 
Marco  Banco  of 
Hamburgh      ==       331-3 
Real     Plate    of 
Spain.             =       10 

P'd.  ster  'g.  in  Ireland=l  0.0=4  10 
Pound  sterling  ...  =1  0.0=4  44  1-2 

COINS,  WEIGHTS,  AND  MEASURES.  gg 

2.  TROY  WEIGHT. 

24  Grains,  marked  grs.  make  1  Pennyweight,  marked  pwt. 

20  Pennyweights       ...     1  Ounce, oz. 

12  Ounces        1  Pound, lb. 

NOTE.    By  Troy  Weight,  all  jewels,  gold,  silver,  electuaries,  and 
liquor?,  are  weighed. 

3.  AVOIRDUPOIS  WEIGHT. 

16  Drains,  marked  drs.  make  1  Ounce, ....  marked  . . .  055. 

16  Ounces 1  Pound,      .      .      .     .      lb. 

28  Pounds 1  Quarter  of  a  cwt.     .     qr. 

4  Quarters 1  hundred cwt.or  11 2lbs. cwt. 

20  Hundred  Weight        .     .     1  Ton,      ....      .      T. 


NOTE  1.    By  this  weight  all  coarse  and  drossy  goods  are  sold,  and 
all  metals,  except  gold  and  silver. 

2.  In  Avoirdupois  Weight  several  other  denominations  are  used  in 
particular  goods  :  viz. 

A  bbl.  of  Pot  Ashes,  =200  Ibs.   {  144  dozen,      .  '   =1  great  gross. 

A  bbl.  of  Pork,      .     =220  Ibs.  $  20  particular  things,  =1  score. 

A  bbl.  of  Beef,      .     =220  Ibs.  $  5  do.               do.      =1  tally. 

A  quintal  of  Fish,  =112  Ibs.  }  24  sheets  of  Paper,  =1  quire. 

12  particular  things,  =1  dozen.  S  20  quires,  .  ...  =1  ream'. 
12  dozen,  .  .  .  =1  gross.  $ 


4.  APOTHECARIES'  WEIGHT. 

20  Grains,  marked  grs.  .  make  1  Scruple,  .  marked  9- 

3  Scruples 1  Dram,  ....  5 

8  Drams 1  Ounce,  ....  § 

12  Ounces 1  Pound,      •     •     •     .  lb 

NOTE.  Apothecaries  mix  their  medicines  by  this  Aveight,  but  buy 
and  sell  their  commodities  by  Avoirdupois.  It  is  the  same  as  Troy 
Weight,  except  its  having  some  different  divisions. 


4  COINS,  WEIGHTS,  AND  MEASURES. 

5.  LONG  MEASURE. 

3    Barley-corns,  marked  bar.  make  1  Inch,  marked  .  in. 
12    Inches  ......     1  Foot,      .....     ft. 

3    Feet    .......   1  Yard,  .....      yd. 

Yards,  or  16-|-  Feet  .     .     1  Rod,  Perch,  or  Pole,  pol. 


8     Furlongs    .....     1  Mile,      ....     mile. 
60    Miles  on  the  equator    .     1  Degree,     ..... 
360     Degrees      .....     1  Great  Circle  of  the  Earth. 

NOTE  1.  This  measure  is  used  to  ascertain  the  distances  of 
places,  or  any  thing  which  has  length  only. 

2.  Distances  are  measured  with  a  chain  4  rods  long,  containing 
100  links. 

3.  4  inches,        =  a  hand.         $        5  feet,    =  a  geometrical  pace. 
6  feet,  =  a  fathom.      $      66  feet,    =a  gunter's  chain. 

3  miles,         =  a  league.       0  "TVVo"  mcn?  =  a  link. 

6.  CLOTH  MEASURE. 

2£  Inches,  marked   in.    make    1  Nail,        marked  n. 

4  Nails    .......     1  Quarter,     .     .     .     .    qr. 

4  Quarters        .....     1  Yard,     .....  yd. 

3  Quarters        .....     1  Flemish  EH,     .       Fl.E. 

5  Quarters        .....     1  English  Ell,     .     .    E.E. 

6  Quarters        .....     1  French  Ell,     .     .    Fr.E. 

4  Quarters        .....     1  Scotch  Ei!,     .     .      S.E. 

7.  TIME. 

60  Seconds,  marked  sec.  make  1  Minute,  marked   m. 

60  Minutes          ......  1  Hour,      .  .  .  h. 

24  Hours         .......  1  Day,       .  .  .  d. 

7  Days     ........  1  Week,     .  .  .  w. 

4  Weeks       .......  1  Month,  .  .  .  mo. 

13  Months,  1  Day,  6  Hours      .  1  Year,      .  .  .  yr. 

365]-  Days     ........  1  Year,      .  .  .  yr. 

52  Weeks       .......  1  Year,      .  .  .  yr. 

100  Years         .......  1  Century,  .  .  C. 

NOTE.  When  the  year  of  the  Christian  Era,  can  be  divided  by  4, 
without  a  remainder,  it  is  then  Bissextile,  or  Leap  Year;  the  remain- 
der, if  any,  shows  what  year  it  is  after  Leap  Year. 


COINS,  WEIGHTS,  AND  MEASURES.  2£ 

8.  CIRCULAR  MOTION. 

60  Seconds,  marked  "  make  1  Prime  or  Minute,  marked  ' 

60  Minutes        1  Degree, 

30  Degrees 1  Sign, S 

12  Signs,  or  360°       .     .     .  1  Circle  of  the  Zodiac. 

NOTE.  The  Zodiac  is  a  space  of  16  degrees  wide,  within  which 
the  motions  of  all  the  planets  are  performed,  except  the  newly  dis- 
covered Asteroids. 

9.  LAND,  OR  SQUARE  MEASURE. 

144  Inches,  marked  in.  make    1  Square  Foot,  marked  ft. 

9  Feet        1  Square  Yard,      .     .     yd. 

30i  Yards,  or  272£  Feet       .     1  Rod, rod. 

40  Poles,  or  Rods      ...     1  Rood,     .     ...     rood. 

4  Roods,  or  160  Rods        .     1  Acre,      ....     acre. 

620  Acres 1  Mile,     ....     mile. 

NOTE.     Land  is  measured  by  the  chain. 

10.  SOLID  MEASURE. 

1728  Inches,  marked     in.    make  1  Solid,  or  Cubic  Foot. 

27  Feet        1  Yard. 

40  Feet  round  timber      ...  1  Ton,  or  Load. 

50  Feet  hewn  timber       ...  1  Ton,  or  Load. 
128  Solid  Feet,  that  is,  8  feet  in") 

length,  4  in  breadth,  and  t 1  Cord  of  Wood. 
4  in  height,     .     .     .     .   J 

NOTE.  All  things  which  have  length,  breadth,  and  depth,  are 
measured  by  Solid  or  Cubic  Measure. 

11.  WINE  MEASURE. 

2  Pints,  marked  pts,  make  1  Quart,      marked     qrt. 

4  Quarts 1  Gallon,  .  .  .  gal. 

42  Gallons  1  Tierce,  .  .  .  tier. 

63  Gallons  1  Hogshead,  .  .  hhd. 

84  Gallons  1  Puncheon,  .  .  pun. 

2  Hogsheads        ....  1  Pipe,  or  Butt,   .  pi.  b. 

2  Pipes 1  Tun,  .  .  .  .  T. 

31i  Gallons  1  Barrel,  .  .  .  bar. 

NOTE.  By  this  measure  all  brandies,  spirits,  perry,  cider,  mead, 
Tinegar,  and  oil,  are  measured, 

3* 


g@  REDUCTION. 

12.  ALE,  OR  BEER  MEASURE. 

2  Pints,  marked     pts.     make  1  Quart,     marked      qrt. 

4  Quarts        1   Gallon,     .     .     .     gal. 

54  Gallons       ......     1    Hogshead  of  beer,  hhd. 

2  Barrels 1   Puncheon,    .     .     pun. 

3  Barrels,  or  2  Hogshead    .     1  Butt,       .     .     .     butt. 

13.  DRY  MEASURE. 

2  Pints,  marked  pts.  make  1  Quart,     marked      qrt. 

4  Gallons        1  Peck,     ....      pc. 

4  Pecks,  or  5  Pecks  water?   .  ^     ,    , 

measure      ...       5   l  Bushel>      '          '     bus« 

*«  32  Bushels 1  Chaldron,       .     .       ch. 

36  Bushels 1  Chaldron  in  London,  ch. 

NOTE.     Salt,  coal,  sand,  fruits,  oysters,  roots,  corn,  and  dry  goods, 
are  measured  by  Dry  Measure. 


REDUCTION. 


REDUCTION  teaches  to  exchange  numbers  of  one  denomi- 
nation to  another,  retaining  the  same  value. 

It  consists  of  two  sorts;  viz.  Descending  and  Ascending, 

CASE  I. 

Reduction  Descending  is  bringing  a  greater  denomina- 
tion into  a  less. 

GENERAL  RULE. 

Multiply  the  highest  denomination  given  by  so  many  of 
the  next  less,  as  make  one  of  that  greater,  and  thus  con- 
tinue to  do  till  the  number  is  brought  into  the  denomination 
o.required. 


REDUCTION.  gv 

EXAMPLES. 

1.  In  £945,  how  many  pence  ? 
£945 

20=shilliugs  in  a  pound. 

18900=shi1Hngs. 

12=pence  in  a  shilling. 

228800=pence.  Ans.  226800. 

PROOF  As  Reduction  Descending  is  performed  by  mul- 
tiplication, «t  is  proved  by  division  ;  that  is.  by  changing 
the  order  of  (be  question,  and  dividing  the  last  product  by 
the  last  multiplier. 

In  the  preceding  question  the  order  will  be.  In  226800 
pence,  how  many  pounds  ? 

Last  mult.  12)226800=last  product. 

2.0)1890,0 


£945  Ans.  as  above.  Ans.  £945. 

CASE  II. 

To  reduce  a  mixt  number  to  a  less  denomination. 
RULE.  Multiply  the  highest  denomination  as  before  di- 
rected, adding  the  less  units,  which   stand  in   the  given 
number  to  the  products,  which  are  of  the  same  name. 

EXAMPLES. 

2.  In  £344     18     4|  how  many  farthings  ? 

20 


6898-{-18  shillings. 
12 


5780-{-4  pence. 
4 


331122+2  farthings.  Ans.  331122  qrf. 

1.  MONEY. 

3.  In  £35,  how  many  shillings  ?  Ans.  700  s. 

4.  In  35  guineas,  how  many  pence  ?  Ans.  11760  d. 

5.  lu  £348     12  '  84-  how  many  farthings  ? 

Ans.  334690  o/s. 


g  REDUCTION. 

2.  TROY   WEIGHT. 

6.  Reduce  149  Ib.  to  grains. 
149 
12 

1788=ounces. 


35760=penayweigh(s. 
24 

143040 
71520 

858240=grs.  *  Ans.  858240  grs. 

7.  In  39     11     12     14  grs.  how  many  grains  ? 

Ans.  230222  grs. 

8.  How  many  grains  are  in  a  silver  tankard,  weighing 
11  Ibs.  ?  Ans.  63360  grs, 

3.  AVOIRDUPOIS  WEIGHT. 

9.  Reduce  49  cwt.  to  ounces. 

49 
'•?&  4 

196=qrs. 

28 

1568 
392 

5488=lb, 
16 

32928 
5488 

87808=oz.  Ans.  87808  oz. 

10.  In     39     2     14     8     4  drs.  how  many  drams  P 

Ans.  11  36260  drs. 

11.  In  12     14     3  qrs.  how  many  pounds  ? 

Ans.  28532  Ib. 

12.  Reduce  8  tons  to  ounces.  Ans.  286720  ozr, 


REDUCTION.  29 

13.  How  many  pounds  are  in  30   hogsheads  of  sugar, 
each  weighing  9|  cwt.  ?  Ans,  31920  lb. 

4.  APOTHECARIES'  WEIGHT. 

14.  In  27     11     7     1     18  grs.  how  many  grains  ? 

12 

335=ounces. 


2687=drams. 
3 

8062=scrupleg. 
20 

161258=grains.  Ans.  161258  grs. 

15.  Reduce  34  Jb.  10  %.  to  drams.  Ans.  3344  drs. 

5.  LONG  MEASURE. 

16.  In  100  miles,  how  many  feet  ? 

100 
8 

800=furlongs. 
40 


32000=rods, 


160000 
16000 


176000=yards. 
3 

528000  Ans.  528000  ft. 

17.  In  84  miles,  how  many  inches  ?       Ans.  5322240  in. 

18.  In  15     7     30     2  feet,  how  many  inches? 

Ans.  1011876  in. 

19.  How  many  rods  in  a  mile  ?  Ans.  320  rods. 

20.  In  100  leagues,  how  many  yards  ? 

Ans.  528000  yds. 

21.  How   many  yards  from  Boston  to  Salem,  the  dis- 
tance being  18  miles  ?  Ans.  31680  yds. 


30  REDUCTION. 

22.  How  many  barley-corns  will  reach  round  the  world  ? 

Ans.  410572800C  bar. 

23.  How  many  inches  from  Boston  to  London,  allowing 
the  distance  3000  miles  ?  Ans.  190080000  in. 


6.  CLOTH  MEASURE. 

24.  In  84  yards,  how  many  nails?  Ans.  1344  n. 

25.  Reduce  124     3     3  nails  to  nails.  Ans.  1999  n. 

26.  In  25  pieces  of  cloth,  each  piece")  f   500yds. 

20  yards,  how  many  yards,  quar    VAns. -s  2000  qrs. 
ters"  and  nails  ?  'J  t8000     n.. 

7.  TIME. 

27.  How  many  hours  in  40  years  ?  Ans.  350400  h. 

28.  In  29     11     36     23  hours,  how  many  seconds  ? 

Ans.  870908400  sec. 

29.  How  many  minutes  since  the  birth  of  our  Saviour, 
the  present  year  being  1818  ?  Ans.  955540800  m. 

•TV".  B.     ±.  To  reduce  Longitude  into  Time. 
RULE.    Multiply  the  Longitude  by  4,  observing  that 
miles  produce  seconds,  and  degrees  minutes  ;  or  divide  the 
longitude  by  15,  the  degrees  equal  to  an  hour. 

EXAMPLES. 

30.  The  Longitude  of  Boston  is  70°  37'  ; 
difference  of  time  between  it  and  London  ? 

70     37 
4 


4     42     28  seconds,  Ans.      Or,  70   37-M   42    28  se. 

2.  To  change  Time  into  Longitude. 
RULE.  Multiply  the  time  by  10,  adding  one  half  of  the 
product  to  itself. 

EXAMPLES. 

31.  In  4    42    28  seconds,  how  many  degrees  of  Longi- 
tude ? 

4     42     28 
10 


|)47     04     40 
23     32     20 

70     37     00  Ans.  70°   37'. 


REDUCTION. 


8.  LAND,  OR  SQUARE  MEASURE. 

32.  In  44  acres,  hovv  many  pi  rein-*  ?         Ans.  7040  per. 

33.  la  49  2   18   pules,  hovv  many  poles?  Ai.s.  7958  pol. 

34.  In  34  acres,  how  iaan>  roods  and  >   A         $     136  roods. 

*'  $5440  rods. 

9.  SOLID  MEASURE. 

35.  In  12  tons  of  round  timber,  how  many  cubic  inches? 

Ans,  8294  10  in. 

30.  Hovv  many  solid  or  cubic  inches  in  12  ions  of  hewn 
timber?  An*.  1036800  in, 

37.  Hovv  many  solid  inches  in  a  cor<J  of  wood  ? 

Aus.  221184  in. 

10.  WINE  MEASURE. 

38.  How  many  gallons  and  pints  in  5  >   »        $    1260  gal. 

Inns  of  wine  ?  S        *'  ?  10080  pts. 

39.  Reduce  5  pipes  to  pints.  Ans.  5040  pts. 

11.  DRY  MEASURE. 

40.  In  30  chaldrons  of  coal,  hovv  many  bushels  ? 

Ans.  960  bush. 

41.  Reduce  24  bushels  to  pints.  Ans.  1536  pts. 

42.  In  20  chaldrons,  hovv  many  bushels.  London  mea- 
sure ?  Ans.  720  bush. 

REDUCTION  ASCENDING. 

REDUCTION  ASCENDING  teaches  to  bring  a  less  denomi- 
nation into  a  greater. 

RULE.  Divide  the  lowest  denomination  given  by  so  many 
of  that  ua.iie  as  make  one  of  the  next  higher;  and  thus 
continue  to  do  till  the  number  is  brought  into  the  denomi- 
nation required. 

PROOF  As  Reduction  Ascending  is  performed  by  divi- 
sion, it  is  proved  by  multiplication  ;  that  is,  by  changing  the 
order  of  the  question,  and  multiplying  the  last  quotient  by 
the  last  divisor,  adding  the  remainders,  if  any. 


g  REDUCTION. 

EXAMPLES. 

1.  MONEY. 

1.  In  752640  farthings,  h«»\v  urxny  pounds  ? 
4)752ri40:=farthings.       Prooi  £  ,34-=last  quotient. 
-  -  20=lA«t  divisor. 

12)188100—  pence. 

15680=shiiliugs. 
12 


784=pounds. 


752640=farthings  as  alicve. 

NOTE.  When  there  are  remainders  after"  dividing-,  they  are 
of  the  same  name  with  their  respective  dividends,  and  mast  be  placed 
after  the  last  quotient,  according  to  the  order  of  their  names,  the 
highest  denomination  first;  the  several  mixt  numbers,  thus  formed, 
will  be  the  answer. 

2.  lu  331122  farthings,  how  many  pounds? 

4)331122 

12)82780     i  qrs.  rem. 
2,0)689,8     4  d.  rem. 


£344   18  4i  Ans.  £344  18  4£. 

3.  In  700  shillings,  how  many  pounds  ?  Ans.  £35. 

4.  In  11760  pence,  how  many  guineas  ?       Ans.  35  guin. 

5.  Bring  334690  farthings  into  pound*-. 

Aus.  £348   12  8i. 
2.  TROY  WEIGHT. 

6.  In  858240  grains,  how  many  pounds  ? 

2,0 

24)858240(3576,0 
72     — 

r 12)1788 

138    

120     149  Ib.  Ans.  149  Ib. 

182 
168 


144 
144 


REDUCTION.  33 

7.  In  230222  grains,  how  many  pounds  ? 

Ans.  39  11   12  14  grs.~ 

8.  How  many  pounds  will  a  tankard  weigh,  which  con- 
-ains  63360  grains  ?  Ans.  1 1  Jb. 

•*.  AVOIRDUPOIS  WEIGHT. 

?.  Reduce  159488  ounces  to  cwt. 

(28)    (4) 
•  16)159488(9968(356 

144          84       

89  cwt 

154        156 
144        140 

108        168 
96       168 

128         0 
128 

0  Ans.  89  cwt." 

.dO.  In  1136260  drams,  how  many  cwt.  ? 

Ans.  39  2  14  8  4  drs. 

11.  How  many  tons  in  28532  pounds  ? 

Ans.  12    14   3  qrs. 

12.  Bring  286720  ounces  to  tons.  Ans.  8  tons. 

13.  How  many  hogsheads,  weighing  9^  each,  are  in 
31920?  "Ans.  SOhhdw 

4.  APOTHECARIES'  WEIGHT. 

14.  Reduce  161253  grains  to  pounds. 

2,0)16125,8 

3)8062   18 


8)2687     1 
12)335  7 


27  11  7  1   18  grs.  Ans.  27  11  7  1   18  grs. 
1ft.  Reduce  3344  drams  to  pounds  ?         Aiis.  34  10  dm 


34  REDUCTION. 

5.  LONG  MEASURE. 

16.  In  528000  feet,  how  many  miles  ? 

3)528000=feet. 

5^)17GOOO=yards. 
4,0)3200,0=rods. 
8)800=furlongs, 

100=miles.  Ans.  100  DL 

17.  In  5322240  inches,  how  many  miles  ?        Aus.  84  m. 

18.  I«  1011876  inches,  how  many  miles  ? 

Ans.  15  7  30  2  2  ft. 

19.  How  many  miles  in  320  rods  ?  Ans.  1  m* 

20.  In  528000  yards,  how  many  leagues?    Ans.  100  Jeag. 

21.  If  31 680  yards  will  reach  from  Salem  to  Boston,  how 
many  miles?  Ans.  18  in. 

22.  If  4105728000  barley-corns  will   reach   round  the 
globe,  how  many  degrees  ?  Ans.  360°. 

23.  Suppose  that  190080000  inches  would  reach  from 
Boston  to  London,  how  many  miles  ?  Ans.  3000  m. 

6.  CLOTH  MEASURE, 

24.  In  1344  nails,  how  many  yards  ?  Ans.  84  yds. 

25.  Reduce  1999  nails  to  yards  ?  Ans.  124  3  3  n. 

26.  Reduce   8000   nails    to    quarters  >   .        f2000qrs. 

-and  yards.  $  I   500  yds. 

7.  TIME. 

27.  How  many  years  in  350400  hours  ?         Ans.  40  yrs. 

28.  In  870908400  seconds,  how  many  years  ? 

Ans.  29   11   3  6  23  h. 

29.  In  955540800  minutes,  how  many  years  ? 

Ans.  1818  yrs, 

8.  LAND,  OR  SQUARE  MEASURE. 

30.  Reduce  7040  rods  to  acres  ?  Ans.  44  acres. 

31.  In  7938  poles,  how  many  acres?  Ans.  49  2  18  pol. 

32.  How  many  acres  in  136  roods?  Ans.  34  acres. 

33.  How  many  acres  in  5140  rods  ?  Ans,  34  acres. 


REDUCTION.  35 

9.  SOLID  MEASURE. 

34.  How  many  tons  of  round  timber  in  829440  solid,  or 
cubic  inches  ?  Ans.  12  tons. 

35.  In  221  1G4  solid  inches,  bow  many  cords  ? 

Alls.  1  cord. 

10.  WINE  MEASURE. 

36.  Reduce  1260  gallons  to  tuns.  Ans.  5  tuns. 

37.  How  many  pipes  in  5040  pints  ?  Ans.  5  pipes. 

11.  DRY  MEASURE. 

38.  In  960  bushels,  how  many  chaldrons  ?     Ans.  30  eh. 

39.  Reduce  1536  pints  to  bushels.  Ans.  24  bush. 

40.  In  720  bushels,  how  many  London  chaldrons  ? 

Ans.  20  ch. 

REDUCTION  ASCENDING  AND  DESCENDING 

Is  exchanging  numbers  from  a  greater  to  a  less,  and  from 
a  less  to  a  greater  denomination,  as  the  nature  of  the  ques- 
tion may  be,  and  is  performed  by  multiplication  and  divi- 
sion. 

EXAMPLES. 
1.  MONEY. 

1.  How  many  shillings,  crowns  "1  f2240  shillings. 

and    pounds    are    in    80  t-  Ans.  •<    336  crowns. 
j  (_    112  pounds. 


2.  In  £84,  how  many  pence,  ^   i  * 

three    pencea."   groats  V  Ans.  ]    *™  three  pences, 
andmoulores?  §  $  ^0  groats. 

'  ^      46  j  moidores. 

3.  A  person  had  20  purse?,  in  each  purse   18  guineas,  8 
pounds,  a  crown,  and  a  moidore;  how  many  pounds  ster- 
ling had  he  ?  Ans.  £530. 

2.  TROY  WEIGHT. 

4.  In  29  o   12  19  grains  Troy,  how  many  pounds  Avoir- 
dupois ?  Ans   24  7  mil 

5.  How  many  rings,  each   weighing  6  8   grs.   may  be 
made  of  4  6   13  pwt.  of  gold? 

Ans.  172  rings,  and  3,  1G  grs.  over. 


36  COMPOUND  ADDITION. 

6.  A  gentleman  sent  a  tankard  to  l»is  goldsmith,  which 
weighed  84  12  pwts   directing  him  to  make  it  into  spoons 
of  3  6  pwts.  each  ?  how  manj  had  he  ? 

Ans.  25  spoons  and  2,  2  pwt  over. 

7.  A  gentleman  sent  his  goldsmith   11   5  6  0   Drains  of 
silver,  and  directed  him  to  make  it  into  tankards  of  1   5   15 
10  grains  each  ;  spoons  of  1   9  11    13  grains  perdnz.  salts 
of  3  10  pwt.  each;  and  forks   of  1   0   11    13  grains  per 
doz  ;  and  for  every  tankard  to  have  one  salt,  a  dozen  of 
spoons,  and  a  dozen  of  forks  ;  what  number  of  each  must 
Le  have  ?  Ans.  2  of  each  sort,  and  899  grs.  over. 

3.    AVOIRDUPOIS  WEIGHT. 

8.  In  34  pounds  Avoirdupois,*  how  many  pounds  Troy? 

Ans.  41  3  16  16  grs. 

9.  How  many  parcels  of  sugar,  of  14  pounds  each,  are 
in  a  hogshead  which  weighs  18  1   14  pounds  ? 

Ans.  147  of  14  Ib.  each. 

4.  LONG  MEASURE. 

10.  How  many  times  the  length  of  a  ship's  keel  will 
reach  from  Boston  to  the  Land's  End,  in  England,  a  direct 
course  being  about  2500  miles,  and  the  ship's  keel   110£ 
feet  in  length?  Ans.  119187££f 

11.  How  many  times  will  the  wheel  of  a  chaise  turn  la 
running  from  Boston  to  Salem,  the  distance  being  18  miles, 
and  tlie  circumference  of  the  wheel  15£  feet? 

Ans.  6131if. 

12.  How  many  steps,  of  2  6  inches  each,  must  a  person 
take  in  walking*  from  Boston  to  Cambridge  Common,  the 
distance  being  3£  miles  ?  Ans.  6864. 


COMPOUND  ADDITION. 

COMPOUND  ADDITION  is  the  collecting  of  several  num- 
bers of  different  denominations  into  one  sum  5  as  pounds, 
shillings  ;  hundreds,  quarters,  &c. 

RULE.  1.  Place  the  numbers  of  the  same  denomination 
under  each  other. 

*  7000  grs.=l  Jb.  Avoirdupois,  and  5760  grs.=  lib.  Troy. 


COMPOUND  ADDITION.  37 

rJ.  Add  the  figures  in  the  lowest  denomination,  as  in  Sim- 
ple Addition. 

3.  Divide  this  sum   by  as  many  of  the  same   name  as 
make  one  of  the  next  higher  denomination,  as  in  Reduction 
Ascending. 

4.  Set  the  remainder   under   the  denomination  added, 
and  carry  the  quotient  to  the  next  higher  denomination ; 
continue  so  to  do  to  the  highest  denomination,  which  add, 
as  in  Simple  Addition. 

NOTE.  This  rule  is  applicable  to  all  sums  in  Compound  Addition 
of  money,  weights  and  i^easures. 

PKOOF.  Cut  off  the  upper  line  of  numbers  by  drawing  .a 
line  below  it ;  add  the  rest  of  the  numbers,  and  set  them 
down  as  in  the  operation  ;  then  add  the  last  1'ound  number 
and  upper  line  together,  their  sum  will  be  the  same  as  the 
first  addition. 


£. 


387  14  11 

87   8 
134   3 


EXAMPLES. 
1.  MONEY. 


£.   s. 
487  12 


9  f 
8  4- 


£1484       5       4 


Sum. 


d.  qrs. 
8  i 


389  18  10  i 

78  19  11  | 

874  13   8  f 


609 


7       5     f 


1484       5       41  Proof. 

NOTE.      4=1  farthing,  or  a  quarter  of  any  thing. 
•5=2  farthings,  or  half  of  any  thing. 
3=3  farthings  or  three  quarters  of  any  thing. 


Ib.  of.  pwt.  grs. 

437  11  18  23 

707  8  14  19 

487  9  16  14 

736  10  18  12 


2.  TROY  WEIGHT. 

lb.  oz.  pwt.  grs. 
983  8  14  13 
487  7  15  12 
787  10  18  15 
148  9  17  13 


lb.  os.  pu-t. 

874  11   14 

987  8  13 

787  10  12 

187  10  16 


2500 


8  20   2408   1 


2838       5     15 


38  COMPOUND  ADDITION. 


3.  AVOIRDUPOIS  WEIGHT. 

cwt.      qrs.    Ib.      oz.     drs.  cwt.      qrs.  Ib.  oz,  dr.- 

345       2     19     13     13  487       1  18  12  12 

749       3     17     14     12  373       2  17  13  14 

300       1        8      14     14  748       3  14  14  !•> 

748       2     14     11      12  874       2  18  13  11 


2144       2573  2484       2     14 


4.  APOTHECARIES'  WEIGHT. 

Ib.  own.     drs.  sent.  Ib.  oun.  drs.  scri{.  grs. 

487  11       6       2  874  10  6       2     18 

787  8        6        1  987  9  4        1     19 

900  732  387  7  3       2     17 

709  11        7       2  487  3  2       1     14 


2886       3       7       1  2737       7208 

5.  LONG  MEASURE. 


.  fur.  pol.  yds.  miles,  fur.  poL  yds.  feet.  in.    bar. 

874     6     36  41  874     4     28  3-1-     2     11     2 

973     4     26  3|  389     5     18  1*      1       81 

187     6     14  li  187     3      17  4f     272 

874     7      18  3  874     1      14  li     1      10     1 


2911      1      16     2^  2325     6     39     3i     0       20 

6.  CLOTH  MEASURE. 


yds.  qrs.  n. 

E.E.  qrs.  n. 

F/.E.  §«.  n. 

Fr.E.  qrs.  n. 

48*7  3  2 

834  4  2 

824  2  2 

879  5  2 

878  1   2 

739  3  1 

347  2  1 

654  4  2 

983  2  1 

487  2  2 

678  1  2 

783  1   1 

756  3  2 

578  3  1 

487  2  1 

874  3  2 

3106     2     3       2640     3     2       2338     2     2       3192     2    3 


COMPOUND  SUBTRACTION. 
7.  TIME. 


mo.  ic. 

d. 

K. 

years,  mo. 

U'. 

d. 

h. 

m. 

874 

11 

3 

6 

23 

837 

8 

3 

5 

18 

33 

784 

8 

1 

5 

19 

478 

9 

2 

6 

22 

39 

130 

7 

1 

4 

12 

748 

11 

3 

5 

13 

24 

898 

6 

2 

1 

15 

874 

o 

1 

6 

14 

13 

2688 

10 

1 

4 

21 

2940 

3 

0 

3 

20 

54 

8. 

MOTION. 

Signs,  deg.  m. 

sec. 

deg. 

TO.  sec. 

dcg. 

m. 

sec. 

9  22 

35 

44 

18 

34  14 

14 

25 

18 

10  13 

19 

18 

17 

36  38 

18 

48 

13 

8  13 

23 

38 

18 

14  17 

12 

13 

18 

11  28 

44 

46 

24 

39  48 

11 

16 

15 

40     18       3     26  79       4     57  56     43 


COMPOUND  SUBTRACTION. 

COMPOUND  SUBTRACTION  teaches  to  find  the  difference 
between  two  numbers  of  different  denominations. 

RULE.  1.  Subtract  the  under  number*  from  the  upper, 
and  set  tbeir  difference  under  their  respective  denomina- 
tions. 

2.  If  the  under  number  of  any  of  the  denominations  is 
greater  than  the  upper,  take  it  from  as  many  as  make  one 
of  the  next  higher  denomination  ;  add  the  difference  to  rhe 
upper  number,  and  set  down  their  sum,  remembering  to 
carry  one  to  the  next  higher  denomination,  before  subtract- 
ing it. 

EXAMPLES. 

1.  MONEY. 

1.  2. 

£.        s.        d.    qrs.  £.        s.       d.    qry. 

8745     10     11     i  Minuend.  483     13     10    1 

189       8       3     I  Subtrahend.  90     17     11    £ 

8556       2       8     i  392     15     10    ± 


40 


COMPOUND  SUBTRACTION. 


2.  TROY  WEIGHT. 


3.  4.  5. 

ib.       os.    pwt.   grs.  Ib.  oz.  pwl.  Ib.  or.    pwl.  grs, 

387      10     13     13  784  8  15  898  7     14     14 

187      11      18      19'  387  11  14  187  10     15     18 


199     10     14     18          396       91          710  8  18     20 

3.  AVOIRDUPOIS  WEIGHT. 

6.  7. 

cu-t.     qrs.   Ib.       oz.     drs.               civt.    qrs.   Ib.  os.  drs. 

437  2  19  13  12      874  2  14  13  13 

C9  3  24  13  14       87  3  27  14  15 


347     2     22     15     14  786     2     14  14     14 

4.  APOTHECARIES'  WEIGHT. 

8.  9.  10. 

Ib.    oun.  drs.  scru.  grs.  Ib.     oun.  drs.  Ib.  oun.  scru.  grs. 

348      10     3     2     12          874       8     4          434     10     3     2 
89     11.    5     2     15  99     10     7          379     11     6     2 


i58     10     5     2     17          774       95  54     10  5     0 

5.  LONG  MEASURE. 

11.  12. 

miles,  fur.  poL    yds.  ft.  miles,  fur.  pol.   yds.  ft.  in. 

387     5     27     2i     1  834     3     25     4£     1  10 

93     6     36     4|     2  87     4     29     3|     2  11 


293     6  30     3       2  746     6     35     5£     1  11 

6.  CLOTH  MEASURE. 

13.  14.  15.  16. 

yds.    grs.  n.  E.Eng.qrs.n.  E.Fl.  qrs.  n.  E.Fr.  qrs.  n. 

431      21  834     4     2  874     21  874  5     1 

139     3     3  89     4     3  89     2     3  87  5     2 

291     22  744     4     3  784     22  786  5     3 


COMPOUND  MULTIPLICATION.  4JI 

7.  TIME. 

17.  18. 

yrs.   mo.  w.  d.   h.   m.   sec.    yrs.   mo.  u\  d.  k.   wf.. 

987  11  2  4  14  13  18   8743   8   1  2  22  14 

374  11  3  5  16  46  55     87   11  3  4  23  56 


612   U  £  5  21   26  23   8660   8  1  4  22  18 


21. 

tun.  hhd.  gal. 

834  1   18 

89  2  28 


hhd. 
834 
87 

19, 

gal. 
1  1 

25 

qrt. 
2 
3 

8. 

pt. 
1 
1 

WINE  MEASURE. 

£0. 
tier.    gal.  qrt. 
38     11      1 
18     24     2 

746 

48 

3 

0 

19     28     3 
QUESTIONS. 

744  2  53 


1.  From  £1  take  '-  qrs.  Ans.  19  11£  qrs. 

2.  From  1  Ib.  Troy,  take  1  grain.       Ans.  11    19  23  grs. 

3.  From  1  cwf.  take  1  oz.  Ans   3  27  15  oz. 

4.  From  a  mile  lake  an  inch.        Ans.  7  39  4^  2  11  in. 

5.  From  a  year  take  a  second. 

Ans.  364  23  59  59  sec. 

5.  T;ike  one  second  from  the   Christian  era,  allowing 
even  years,  and  365  days  for  a  year. 

Ans.  1817  364  23  59  59. 


COMPOUND  MULTIPLICATION. 

COMPOUND  MULTIPLICATION  is  the  multiplying  of  sums 
of  different  denominations. 

RULE.  Multiply  the  lowest  denomination  by  the  given 
multiplier,  and  divide  the  product  by  as  many  as  make  one 
of  the  next  higher  denomination  ;  set  down  the  remainder, 
and  add  the  quotient  to  the  next  higher  denomination,  after 
it  is  multiplied. 

PROOF,     By  Division. 


4#  COMPOUND  MULTIPLICATION. 

EXAMPLES. 
J.  MONEY. 

1.  2. 

£.        $•  d.  qrs.  £.         s.  d,    qrs, 

Multiply  874     10  6     i  8343     18  11     £ 
by                           8                                                    12 

C996       4     4        Product.     100187       7       9 

2.  TROY  WEIGHT. 

2.  4. 

Z6.        o£.  jpu7.     grs.  Ib.     os.  j?w/.  gr^, 

Multiply  874     10  12     11  343     8     8     3  by  24. 

by  9  4X6 

7873     11      12     3  8248     9   15     0 

3.     AVOIRDUPOIS  WEIGHT. 
5.  6. 

civt.     qrs.     Ib.     os.  cwt.    qrs.  Ib.     oz. 

Multiply       28     2     14     12  37     3     18     2  by  16. 

by  11  4X4 

314     3     22       4  606     2     10     0 

4.     APOTHECARIES'  WEIGHT. 

7.  8. 

Ib.  oun.drs.  scru.  Ib.     oun.drs,  scru. 

Multiply     18     11     5  2  804     8     3     2  by    3G. 
by                           8  6X6 

151       951  28969     440 

5.     LONG  MEASURE. 

9.  10. 

milts,  fur.  pol.  yds.  miles,  fur.  pol.  yds. 

Multiply     34     3     10     4£  80     7     34     3 

by  7  10 

240     6     35     4  809     6     25     2 


COMPOUND  MULTIPLICATION.  43 

6.   TIME. 

11.  12. 

Multiply  34     11     2     3     12           87    10    3    2  12    10    18 

by                              12  12 

419       7200       1054     10    0    2  2      3    36 


Compound  Multiplication  is  an  useful  and  concise  rule 
for  finding  the  value  of  goods.  It  is  a  contraction  of  the 
Rule  of  Three,  when  the  first  number  is  an  unit. 


GENERAL  RULE. 
Multiply  the  price  by  the  quantity. 


CASE.  I. 

When  the  quantity  is  not  more  than  12. 
Multiply  the  price  1 
the  product  will  be  the  answer. 

EXAMPLES. 


RULE.  Multiply  the  price  by  the  whole  quantity,  and 
"I  be 


1.  What  will  8  yards  of  cloth  cost  at  £3  12  6£  per 
yard  ? 

£3     12     6i 
8 


£29       0     4  AIJS.  £  29  0  4. 

2.  What  will  12  Ib.  of  tea  cost  at  £0  13  84-  per  pound  ? 

Ans.  £8  4  6. 

CASE  II. 

When  the  quantity  is  more  than  12,  and  a  composite 
number,  that  is,  such  that  two  figures  will  make  it  when, 
multiplied  together. 

RULE.  Find  two  figures  which  will  make  the  quantify 
when  multiplied  together,  arid  multiply  the  price  by  these 
figures,  the  last  product  will  be  the  answer. 


44  COMPOUND  MULTIPLICATION, 

EXAMPLES. 

3.  What  will  24  yards  cost  at  £4  10  8|-  per  yard  ? 

i=price.J 
4  yards. 

18       2     10=value  of  4  yards. 
6  yards. 


£108     17  =    value  of  24  yards. 

Ans.  £108  17. 

4.  What  will  132  yards  cost  at  £3  0  8{  per  yard  ? 

Ans.  £400  10  9, 

CASE  III. 

When  the  quantity  is  such  that  no  figures  in  the  table 
will  make  it. 

RULE.  Multiply  hy  two  such  figures  that  will  come  the 
nearest  to  it,  and  add  the  price  of  the  odd  quantity,  if  less, 
but  subtract  it.  if  greater. 

EXAMPLES. 

5.  What  will  29  Ib.  cost,  at  £2  8  4£  per  Ib.  ? 
4x7=28  nearest.         £2       8       4£=price. 

1  odd.  4  Ibs. 


29  Ib.  9     13       6  =value  of  4  Ibs. 

7 


67     14       6  =value  of  28  Ibs. 
Q       o       4i_  Rvalue  of  1  Ib.  add- 
2      £ed,  because  less. 


70       2     10i=value  29  Ibs. 

Ans.  £70  2  101. 
6.  What  will  127  yards  cost  at  £8  0  Of. 

Ans.  £1016  7   11|, 

CASE  IV. 

To  find  the  value  of  a  hundred  weight. 
•RULE.    Multiply  the  price  by  7,  its  product  by  8,  and 
this  product  by  2,  the  last  will  be  the  answer. 


COMPOUND  MULTIPLICATION. 


EXAMPLES. 

T.  What  will  1  cwt.  cost  at  £3  10  4!  per  lb.? 

3     10     4i 

7 


24     12     7i=value  of  7  lb. 


197       10  =valueof  56  lb. 


£394       2    0  =value  of  1  cwt.  or  112  lb. 

Ans.  £394  5. 
5.  What  costs  1  cwt.  at  £3  0  8f  per  lb.  ? 

Ans.  £340  1  8. 

CASE  V. 

To  find  the  value  of  two  or  more  hundreds. 

RULE.  First  find  the  value  of  one  hundred  weight,  (by 
Case  IV.)  then  multiply  the  price  of  one  hundred  weight 
by  the  given  number  of  hundreds. 

EXAMPLES. 

9.  What  will  12  cwt.  cost  at  £3  8  41  per  lb.  f 

3       8     41 

7 


23     18     7i=value  of  7  lb. 
8" 


191       9     0=value  56  lb. 


382     18     0=value  1  cwt. 

12=given  hundreds. 


£4594     16     0=12  cwt.  Ans.  £4594  16. 

10.  What  will  87  cwt.  cost  at  £l   13  44-  per'lb  ? 

Ans,  £16260  6. 

5 


£6  COMPOUND  DIVISION. 

CASE  VI. 
When  there  is  a  fractional  part  in  the  quantity. 

RULE.  1.  Find  the  value  of  the  whole  numbers  by  the 
preceding  rules,  according  to  the  question. 

2.  Multiply  the  price  by  the  numerator,  and  divide  the 
product  by  the  denominator;  the  quotient  will  be  the  value 
of  the  fraction,  which,  added  together,  will  be  the  value  of 
the  whole  quantity.  (See  Case  VII.  in  Simple  Division.) 

EXAMPLES. 
11.  What  will  8i  yards  cost  at  £3  2  GI  per  yard  ? 

i)3       2     6i 
8 


25       0     4  =value  of  8  yards. 
1     11     3i=value  1  yard. 


£26     11     7±=value  Bk  yards.         Ans.  £26  11   7j. 
12.  AVhat  will  144f  yards  cost  at  £2    18    3|  per  yard  ? 

Ans.  £420  15 


COMPOUND  DIVISION. 

COMPOUND  DIVISION  is  the  dividing  of  sums  of  different 
denominations. 

RULE.  Divide  the  highest  denomination  by  the  given 
number,  and  if  any  thing  remains,  reduce  it  to  the  next 
lower  denomination,  by  multiplying  it  by  as  many  of  the 
next  less  as  make  one  of  that  name,  adding  to  the  product, 
the  number,  if  any,  in  the  next  lower  denomination,  and 
divide  as  before,  selling  each  quotient  under  its  respective 
denomination. 

PROOF.     By  Multiplication. 

EXAMPLES. 

1.  MONEY. 

1.  2. 

Divide     £384     18     4  by  8.  £387     13     4Jbyl2. 

8)384     18     4    '  12)387      13     4A    " 


£48       2     3^  Ans.  £32       6     1^  Ans. 


COMPOUND   DIVISION.  47 

2.  TROY  WEIGHT. 

3.  4. 

lb.     oz.   put.  grs.  lb.  os.  pwt.  grs. 

Divide     9     11      13     14  by  8.  18  8     12  13byl2. 

8)9     11      13     14  12)18  8      12  13 

1        2     19       4+6  1      6     14       9+1 

3.  AVOIRDUPOIS  WEIGHT. 

5.  6. 

cwt.  qrs.    lb.  cwt.    qrs.    lb.      os.     drs. 

Divide8)84     2     18by8.     11)874     3     27     13    13byll. 

10     2       9  4  79     2       5       1        4+1 

4.  APOTHECARIES'  WEIGHT. 

7.  8. 

lb.  ou.drs.scr.  lb.      ou.  drs.scr.grs. 

Divide  7)134    9    3    2  by  7.          8)874    10   5    2    14byC. 

19    3    0    1    11+3  109      422      4+2 

5.  LONG  MEASURE. 
9.  10. 

miles.  fur.pol:yds.ft.  miles,  fur.pol.yds.ft. 

Divide  12)384    6    24   3    2  by  12.     9)874    7    34   3   2  by  9. 


32   0    22    0    0  11  in.          97    1    30    2    2  6  2 

6.  TIME. 

11.  12. 

yrs.  mo.  w.  d.  h.    m.  sec.         yrs.  mo.  w.  d.   h. 
Divide  11)874  11   2  3  18  43  24     9)874  11    1   4  22 


79     620     8   14  51+3     97     2  2  2  21   6  40 

COMPOUND  DIVISION  is  useful  in  finding  the  value  of  1 
lb.  1  yard,  &c.  having  the  value  and  the  quantity  given. 


4g  COMPOUND  DIVISION. 

It  is  a  contraction  of  the  Rule  of  Three,  when  the  third 
term  is  an  unit. 

GENERAL  RULE. 

Divide  the  price  by  the  quantity,  and  the  quotient  will 
be  the  answer. 


CASE  I. 

When  the  quantity  does  not  exceed  12. 
RULE.  Divide  the  price  by  the  whole  quantity. 

EXAMPLES. 

1.  If  8  yards  cost  £29  0  4,  what  will  1  yard  cost  ? 

8)29       0     4 

£3     12     6|  Ans.  £3  12  6£. 

2.  If  12  Ib.  cost  £8  4  6,  what  will  1  Ib.  cost? 

Aus.  £0  13  8i. 

CASE  II. 

When  the  quantity  is  more  than  12,  and  such  a  number 
that  two  or  more  figures  will  make  it,  when  multiplied  to- 
gether. 

RULE.  Divide  the  price  by  these  figures,  and  the  last 
quotient  will  be  the  answer. 

EXAMPLES. 

3.  If  24  yards  cost  £108  17,  what  will  1  yard  cost  ? 

4X6=24.  4)108     17 

6)27       4     3 


£4     10     8£         Ans.  £4  10  8^ 

4.  If  132  Ib.  cost  £400  10  9,  what  will  1  Ib.  cost? 

Ans.  £3  0  8| 


COMPOUND  DIVISION.  49 

CASE  III. 

When  the  quantity  is  such  that  no  two  figures  in  the 
Table  will  make  it. 

RULE.  Divide  the  whole  price  by  the  whole  quantity,  as 
in  Long  Division. 

EXAMPLES. 

5.  If  29  yards  cost  £70  2  10£,  what  will  1  yard  cost? 

29)70     2     10|     (2     8     4|  Ans. 
58 

12 

20 

29)242 
232 

10 
12 

29)130 
116 

14 
4 

29)58 
58 

0  Ans.  £2  8  4|. 

6.  If  127  yards  cost  £1016    7    11^,  what  will  1  yard 
cost?  Ans.  £8  Q  Of. 


CASE  IV. 

When  the  quantity  is  one  hundred  weight,  to  find  the 
value  of  1  Ib. 

RULE.  Divide  the  price  by  8,  its  quotient  by  7,  and  this 
quotient  by  2,  the  last  quotient  will  be  the  answer. 

5* 


0Q  COMPOUND  DIVISION. 

EXAMPLES. 

7.  If  one  hundred  weight  cost   £394  2  what  will  one 
pound  cost  ? 

8)394     2 

7)49     5   -3 
2)7     0     9 

£3  10     4$  Ans.  £3  10  4$. 

8.  If  one  hundred  weight  cost  £340  1  8,  what  will  one 
pound  cost  ?  Ans.  £3  0  8|. 

CASE  V. 

When  the  quantity  is  two  or  more  hundreds  to  find  the 
price  of  one  pound.  ' 

RULE.  Divide  the -given  price  hy  the  given  number  of 
hundreds,  the  quotient  will  be  the  price  of  one  hundred 
weight,  then  divide  by  8,  7  and  2,  the  last  quotient  will  be 
the  price  of  one  pound. 

EXAMPLES. 

9.  If  12  cwt.  cost  £4594  16,  what  will  1  Ib.  cost? 

12)4594     16 


8)382     18 
7)47     18     3 
2)6     16     9 


£3       8     4|  Ans.  £3  8  4i. 

10.  If  87  cwt.  cost  £16260  6,  what  will  1  Ib.  cost  ? 

Ans.  £1   13  4i. 

CASE  VI. 

When  there  is  a  fractional  part  in  the  quantify. 
RULE.  Multiply  the  integer  of  the  given  quantity  by 
the  denominator  of  the  fraction,  and  to  the  product  add  the 
numerator,  for  a  divisor;  multiply  the  given  price  by  the 
denominator,  and  divide  by  the  new  divisor,  the  quotient 
will  be  the  answer.  (See  Case  YI.  iu  Simple  Division.) 


VULGAR  FRACTIONS.  5^ 

EXAMPLES. 

11.  If  8i  yards  cost  £26  11  7i,  what  will  1  yard  cost? 
8i  26     11     7i 

2~  2 


17=y.          17)53       3     2^(3     2     GI 
51 

2 
20 

17)43 
34 

9 

12 

17)110 
102 

8 
4 

17)34 
34 

0  Ans.  £3  2  6£. 

12.  If  144f  yards  cost  £420  15  10i-f  1,  what  will  1  yard 

cost?  Ans.  £2  18  3i. 


VULGAR  FRACTIONS. 

1.  A  FRACTION  is  a  part,  or  parts,  of  an  unit. 

2.  A  fraction  is  written  with  two  numbers,  placed  one 
above  the  other,  with  a  line  drawn  between  them  ;  as  f . 

3.  The  number   above  the  line  is  called  the  na-\^ 
merator.  r 

4.  The  number  below  the  line  is  called  the  denomi-f  ~ 
nator. 

5.  The  denominator  shows  into  how  many  parts  the  unit 
is  divided,  and  the  numerator  how  many  of  these  parts  are 
expressed,  or  meant  by  the  fraction* 


5«J  VULGAR  FRACTIONS. 

6.  A  fraction  Las  its  origin  from  Division,  the  numera- 
tor being  the  remainder,  and  the  denominator  the  divisor. 
(See  Note  in  Simple  Division,  jmge  18.) 

7.  The  numerator  of  a  fraction  is  to  he  considered  as  a 
dividend,  and  the  denominator  as  a  divisor,  and  the  frac- 
tion as  an  expression  of  the  quotient,  arising  from  the  divi- 
sion of  the  nu/nerator  by  the  denominator.     Hence, 

8.  A  fraction  is  less,  equal,  or  greater  than  an  unit,  as 
the  numerator  is  less,  equal,  or  greater  than  the  denomi- 
nator. 

9.  The  nature  of  a  fraction  may  be  illustrated  by  the 
following  example.     Let  11  be  divided  by  3. 

3)11 


The  quotient  is  three  whole  units,  the  remainder  signifies 
that  the  2  is  divided  by  3,  and  that  the  quotient  is  f 
of  an  unit. 

10.  A  vulgar  fraction  is  that  which  can  have  any  denom- 
inator, and  may  be    either  proper,  improper,  compound, 
or  mixt. 

11.  A  proper,  single,  or  simple  fraction  is  that  whose 
numerator  is  less  than  its  denominator;  as  f. 

12.  An  improper  fraction  is  that  whose  numerator  is 
greater  than  its  denominator  ;  as  f  . 

13.  A  compound  fraction  is  a  fraction  of  a  fraction,  and 
is  connected  by  the  word  o/;  as  |  of  %  of  f  . 

14.  A  mixt  number,  or  fraction,  is  composed  of  a  whole 
number  and  a  fraction;  as  5J. 

15.  The  value  of  a  fraction  depends  on  the  proportion 
which  the  numerator  has  to  the  denominator  ;  therefore  the 
same  fraction  may  be  expressed  by  many  different  num- 
hers  ;  as  TYo>  ?f  »  If  >  If  »  T62»  f  •  j  are  alt  equal  fractions, 
each  being  equal  to  one  half  of  an  unit. 

16.  When  the  numerator  and  denominator  are  alike,  the 
fraction  is  equal  to  1. 

17.  A  fraction  whose  numerator  is  greater  than  its  de- 
nominator, is   equal  to  some  whole,  or  rnixt   number;  as 

3=*f 

18.  A  whole  number  may  be  expressed  fractionally  by 
placing  1  under  it  ;  as  ^=to  4. 

NOTE.  As  fractions  can  neither  be  added,  subtracted,  multiplied, 
nor  divided,  before  they  change  their  forms  by  Reduction,  it  is  neces- 
sary that  this  rule  should  be  explained  before  Addition. 


VULGAR  FRACTIONS.  53 

REDUCTION  OF  VULGAR  FRACTIONS. 
Reduction  of  fractions   teaches    to    bring   them    from 
one  form  into  another,  to  prepare  them  for  the  operations 
of  Addition,  Subtraction,  Multiplication  and  Division. 

PROBLEM  I. 

To  find  the  greatest  common  measure  of  any  two  numbers. 

RULE.  Divide  the  greater  number  by  the  less,  and  the 
last  divisor  by  the  remainder,  till  nothing  remains  ;  the  last 
divisor  will  be  the  greatest  common  measure. 

NOTE.  A  number  which  can  divide  several  numbers  exactly,  is 
called  their  common  measure. 

EXAMPLES. 

1.  To  find  the  greatest  common  measure  of  48  and  256. 

48)256(5 
240 

16)48(3 
48 

0 

16  being  the  last  divisor,  is  the  greatest  common  measure. 

Ans.  16. 

2.  Find  the  greatest  common  measure  of  216  and  768. 

Ans.  24. 
PROBLEM  II. 

To  find  the  greatest  common  measure  of  three  or  more 
numbers. 

RULE.  Find  the  greatest  common  measure  of  the  two 
least  given  numbers ;  then  find  the  common  measure  of  this 
measure,  and  the  next  greater  of  the  given  numbers,  and 
again  of  this  last  measure,  and  the  next  greater,  and  so  on 
till  all  the  given  numbers  are  used. 

EXAMPLES. 

3.  Find  the  greatest  common  measure  of  48,  80,  and  136. 
80-:-48=16  and  136-r-16=8=greatest  common  measure. 

Ans.  8. 

4.  What  is  the  greatest  common  measure  of  216,  270, 
and  405.  Ans.  27. 

PROBLEM  III. 
To  find  the  least  common  multiple  of  several  numbers. 


04  VULGAR  FRACTIONS. 

RULE.  Set  the  numbers  in  a  line,  and  divide  them  by  any 
number  which  will  divide  two  or  more  of  them  \vithout  a 
remainder  ;  place  the  quotients  and  the  undivided  numbers 
in  a  line  under  them;  divide  them  continually  as  before, 
until  it  appears  that  no  two  can  be  divided ;  the  continual 
product  of  all  the  undivided  numbers,  and  the  several  divi- 
sors, will  be  the  least  common  multiple  required. 

NOTE.  A  common  multiple  is  a  number  which  can  be  divided  by 
two  or  more  numbers. 

EXAMPLES. 

5.  What  is  the  least  common  multiple  of  2,  3,  6,  9,  12, 
and  15  ? 

332     3     6     9   12  15 

2)2     1     2     3     4     5 

11132     5X2X3X2X3=180.         Ans.  180. 

6.  What  is  the  least  common  multiple  of  the  nine  digits  ? 

Ans,  2520. 
CASE  I. 

To  reduce  fractions  to  their  lowest  terms. 
RULE.  Divide  the  numerator  and  denominator  of  the 
given  fraction  by  any  number  which  will  divide  them  with- 
out a  remainder,  and  so  on  till  there  is  no  number  greater 
than  an  unit,  which  will  divide  them.  Or  divide  the  nu- 
merator arid  denominator  by  their  greatest  common  mea- 
sure, and  the  quotients  will  form  the  fraction  in  its  lowest 
terms. 

NOTE.  If  the  common  measure  happens  to  be  1,  the  fraction  is 
in  its  lowest  terms. 

EXAMPLES. 

7.  Reduce  /•£$  to  its  lowest  terms. 

Or     96)544(5 

480     com.  meas.  32)IV?=T3T  as  before. 

64)96(1 
64 


=T3T  Ans.   32(64(2 
64 


Ans. 


VULGAR  FRACTIONS. 


3.  Reduce  f  f  -ff  .  to  its  lowest  terms.  Ans.  £. 

9.  jVyW  to  its  lowest  terms.  Ans.  |-. 


CASE  II. 

To  reduce    a  mixt    number  to    its    equivalent  improper 

fraction. 

RULE.  Multiply  the  whole  number  by  the  denominator 
of  the  given  fraction,  add  the  numerator  to  the  product  for 
a  new  numerator,  which  written  over  the  denominator  will 
form  the  fraction  required. 

EXAMPLES. 

10.  Reduce  12f  to  an  improper  fraction. 

12 
8     denominator. 

96 
3  numerator  added.     And    99  new  num. 

99  new  numerator.  8  denom.     Ans.  -/t 

11.  Reduce  120  ji  to  an  improper  fraction.       Ans.  ^f1. 

CASE  III. 

To  reduce  an  improper  fraction  to  its  equivalent  whole 

or  mixt  number. 

RULE.  Divide  the  numerator  by  the  denominator,  the 
quotient  will  be  the  whole  number,  and  the  remainder,  ii* 
any,  placed  over  the  given  denominator  will  form  the  frac- 
tional part. 

EXAMPLES. 

12.  Reduce  9¥9  to  a  whole  or  mixt  number. 

8)99 

12f.  Ans.  12f. 

13.  Reduce  1ff1  to  a  whole  or  mixt  number. 

Ans.  120ft. 

CASE  IV. 

To  reduce  a  whole  number  to   a  vulgar  fraction,  whose 

denominator  shall  be  given. 

RULE.  Multiply  the  whole  number  by  the  given  denom- 
inator for  the  numerator,  which,  placed  over  the  given  de- 
nominator, will  form  the  fraction  required, 


06  VULGAR  FRACTIONS. 

,  EXAMPLES. 

14*     Reduce  3  to  a  fraction  whose  denominator  shall  be  4. 
3X4=12.  And  V2=Ans. 

15.  Reduce  12  to  a  fraction  whose  denominator  is  11. 

Ans.  V¥- 

CASE  V. 

To  reduce  a  compound  fraction  to  a  simple  one. 
RULE.     Multiply    all  the   numerators    continually  to- 
gether for  a  new  numerator,  and  all  the  denominators  for  a 
new  denominator  of  the  simple  fraction. 

EXAMPLES. 

16.  Reduce  \  of  £  of  f  to  a  simple  fraction. 
1X3X5=15  new  numerator.        .     ,  is_An(     15 
2X4X8=64  new  denominator.    J     d  «?-Ans-  * *• 

17.  Reduce  f  of  f  of  8  to  a  simple  fraction.         Ans.  2f. 

CASE  VI. 

To  reduce  fractions  of  different  denominators  to  fractions 

having  a  common  denominator. 

RULE.  Multiply  each  numerator,  taken  separately,  in- 
to all  the  denominators,  except  its  own,  for  new  numera- 
tors ;  then  multiply  all  the  denominators  continually  to- 
gether for  the  common  denominator. 

NOTE.  When  there  are  integers,  mixt  numbers,  or  compound  frac- 
tions, given  in  the  question,  they  must  first  be  reduced  to  their  sim- 
ple forms  by  their  proper  rules. 


EXAMPLES. 

18.  Reduce  f ,  f ,  and  f  to  fractions  having  a  common  de- 
nominator. 

3X8X7=1681 

5x4x7=140  I  new  numerators. 

6X8X4=192 J  And  fff   iff  |4|=Ans. 

4x8x7=224  common  denominator. 

19.  Reduce  f,  f-  off,  and  f  to  fractions  having  a  com- 
mon denominator.  Ans.  ff|,  |f |,  |||. 
2CU,    Reduce  f ,  f  and  7|  to  a  common  denominator. 

Ans,  Iff,  A°o,  VVV- 


VULGAR  FRACTIONS.  $y 

21.     Reduce  £,  f,  -2  of  T3T,  and  ~  of  14f  to  a  common  de- 
nominator. Ans.  -.' 


CASE  VII. 

To  reduce  any  fractions  to  others,  which  shall  have  the 

least  common  denominator. 

RULE.  Find  the  least  common  multiple  (by  prob.  3d)  of 
all  the  denominators  of  the  given  fractions,  and  it  will  be 
the  common  denominator  required ;  divide  the  common  de- 
nominator by.  the  denominator  of  each  fraction,  and  multi- 
ply the  quotient  by  the  numerator,  the  product  will  be  the 
numerator  of  the  fraction  required. 

EXAMPLES. 

22.  Reduce  £,  f ,  and  -f-  to  fractions  having  the  least  com- 
mon denominator. 

2)4     8     7=denominators. 

2)2     4     7 

1     2     7x2x2x2=56  least  com.  multiple.=to  the  least 
common  denominator. 

Then  56-^-4x3=42   first  numerator. 
56-^-8x5=35  second      do. 
56-^-7x6=48  third         do. 

Whence,  |f,  |f,  I-*.  Au«. 

23.  Reduce  |,  f ,  £  and  £  to  fractions  with  the  least  com- 
mon denominator.  Ans.  ££, 

CASE  VIII. 

To  reduce   a  given  fraction  to  another  equal    to  it,  that 

shall  have  a  given  denominator. 

RULE.  Multiply  the  numerator  by  the  given  denomina- 
tor, and  divide  the  product  by  the  former  denominator  5  the 
quotient,  written  over  the  given  denominator,  will  form 
the  fraction  required. 

EXAMPLES. 

24.  Reduce  f  to  a  fraction  of  the  same  value,  whose  de 
nominator  shall  be  12. 

2xl2=24-f-3=8,  And  -,-%  Aus. 

6 


58  VULGAR  FRACTIONS. 

25.  Reduce  f  to  a  fraction  of  equal  value,  whose  denom- 
inator is  9.  Aus.     7£ 

9=rf' 
CASE  IX. 

To  reduce  a  given  fraction  to  another  equal  to  if,  that  shall 

have  a  given  denominator. 

RULE.  Multiply  the  denominator  by  the  given  numera- 
tor, and  divide  the  product  by  the  former  numerator,  the 
quotient,  written  under  the  given  numerator,  will  form  the 
fraction  required. 

EXAMPLES. 

26.  Reduce  f  to  a  fraction  of  the  same  value  whose  nu- 
merator shall  be  12. 

12x3-^-2=18.     And  ||.  Ans. 

27.  Reduce"  f  to  a'  fraction  of  the  same  value  whose  nu- 
merator shall  be  15.  Ans.J^f. 

CASE  X. 

To  reduce  fractions  from  a  less  denomination  to  a  greater  / 

retaining  the  same  value. 

RULE.  Make  the  given  fraction  a  compound  one  by 
comparing  it  between  the  denomination  given  and  that  to 
which  it  is  to  be  reduced  ;  then  reduce  this  compound  frac- 
tion to  a  simple  one. 

EXAMPLES. 

28.  Reduce  £  of  a  farthing  to  the  fraction  of  a  pound. 

4  of  i  of  TV  of  A;  then  /^^fe  }  ***  «  =  >  >  -  Ans* 

29.  Reduce  f  of  a  penny  to  the  fraction  of  a  pound. 


30.  Reduce  f  of  a  pennyweight  to  the  fraction  of  a  pound 
Troy.  Ans.  ^Ib. 

31.  Reduce  f  of  an  ounce  to  the  fraction  of  a  cwt. 

Ans.  ^T¥  cwt. 

32.  Reduce  |  of  an  inch  to  the  fraction  of  a  mile. 

Ans.  T^g-jo-  ^* 

33.  Reduce  J  of  a  nail  to  the  fraction  of  a  yard. 

Ans.  G\  yd. 

34.  Reduce  J  of  a  minute  to  the  fraction  of  a  year. 

Aug.  ^  ear, 


VULGAR  FRACTIONS.  59 

CASE  XI. 

To  reduce  fractions  from  a  greater  denomination  to  a  less, 

retaining  the  same  value. 

RULE.  Multiply  the  numerator  of  the  given  fraction  by 
the  parts  contained  in  all  the  denominations  between  if, 
and  that,  to  which  it  is  to  be  reduced,  for  a  new  numerator, 
which,  placed  over  the  denominator  of  the  given  fraction, 
will  form  the  fraction  required. 

EXAMPLES. 
35.     Reduce  TSTT  °^  a  pound  to  the  fraction  of  a  farthing. 


36.  Reduce  3^  of  a  pound    to  the  fraction  of  a  penny. 

Ans.  |d. 

37.  Reduce  ^|¥  of  a  pound  Troy  to  the  fraction  of  a  pen- 
nyweight. Ans.  f  pwt. 

38.  Reduce  ^|7T  of  a  cwt.  to  the  fraction  of  an  ounce. 

Ans.  £•  oz. 

39.  Reduce  TTT^TO"  °f  a  m^e  to  the  fraction  of  an  inch. 

Ans.  f  in. 

40.  Reduce  6-4  of  a  yard  to  the  fraction  of  a  nail. 

Ans.  f  nail. 

41.  Reduce  asr!?^  °f  a  vear  to  the  fraction  of  a  minute. 

Ans.  •£  min. 

CASE  XII. 

To  reduce  a  mia^t  fraction  to  a  simple  one. 
RULE.     1.  When  the  numerator  is  a  mixt  number,   re- 
duce it  to  an  improper  fraction  ;  then  multiply  the  denom- 
inator of  the  fraction  by  the  denominator  of  the  fractional 
part  for  a  new  denominator. 

EXAMPLES. 

42.  Reduce  to  a  single  fraction. 

48 
36x3+2=110  numerator. 

48x3=      144  new  denominator.     And  }^=f4  An*. 

2.     When  the  denominator  is  a  mixt  number,  reduce 
it  as  before,  then  multiply  the  numerator  of  the  fraction  bv 


60  VULGAR  FRACTIONS. 

the  denominator  of  the  fractional  part  for  a  new  numera- 
tor. 

47 

43.  Reduce  to  a  simple  fraction. 

65! 

65x5-1-4=329  denominator.          A    .   o~r_r   A 
47X5=      235  new  numerator.      Ar 

CASE  XIII. 

To  reduce  any  mixt  quantity  of  coins,  weights  or  meas- 
ure to  the  simple  fraction  of  an  integer. 
RULE.     Reduce  the  given  number  to  the  lowest  denom- 
ination in  it  for  the  numerator,  and  the  integer  to  the  same 
denomination  for  the  denominator  of  the  fraction  required. 

s.    d. 

41.     Reduce  18  4^  to  the  fraction  of  a  pound. 
#.    d. 

18  41  20 

12  12 

220  240 

4  4  Andfff={-H£Ans, 

882  numerator.     960  denom. 

45.     Reduce  8  7  p\vt.  to  the  fraction  of  a  Ib.  Troy. 

Ans.  if  I  Ib. 

16.  Reduce  3  14  12  7  drs.  to  the  fraction  of  a  cwt 

Ans.  Iff  if  cwt. 

17.  Reduce  7  34   1  2  11  inches  (o  the  fraction  of  a  mile. 

Ans.  |||p  mile. 

-13.     Reduce  145  18  40  13f  seconds   to  the  fraction  of  a 
vear.  Ans.  fVYsVeWc  year* 


CASE  XIV. 

To  find  the  value  of  a  fraction. 

RULE.  Multiply  the  numerator  of  the  given  fraction  by 
the  parts  contained  in  the  next  less  denomination,  and  di- 
vide the  product  by  the  denominator,  and  thus  continue 
to  do  till  the  fraction  is  reduced  to  the  lowest  denomina- 


VULGAR FRACTIONS.  (>1 

EXAMPLES. 

49.  What  is  the  value  of  4  of  a  pound  r 

4 
20 

7)80(11   51d. 

77 

3 
12 

36 
35 

~T  Ans.  11   5i  d. 

questions.  Answers. 

50.  What  is  the  value  of  4  of  a  guinea  ?          12  5i-fi  qrs. 

51 ^ofacwl?  3181010|drs. 

52 2-0f  a  mile  ?  68428  in. 

53 I  of  a  yard  ?  3  2  n. 

54 fhhd.ofale?  21   2|  qrs. 

55 £  of  a  year  ?  9   1   2  8  h. 

56 |  of  a  month?  3  3  12  li. 

ADDITION  OF  VULGAR  FRACTIONS. 

RULE.  1.  Reduce  compound  fractions  to  simple  ones; 
mixt  numbers  to  improper  fractions  ;  fractions  of  different 
denominations  to  the  same,  and  all  of  them  to  a  common 
denominator. 

2.  Add  all  the  numerators  together,  and  place  their  sum 
over  the  common  denominator. 

PROOF.  Find  the  value1  of  the  given  fractions  severally  and  add 
them  together  ;  then  find  the  value  of  the  fraction  making  the  an- 
swer ;  if  they  agree,  the  work  is  right. 

EXAMPLES. 

57.     Add  f  and  f  together. 
3X5=15 
4X4=16 

31=sum  numerators.    And  fi—HJ.  AHS, 
4X5=20  denominator. 
6* 


62  VULGAR  FRACTIONS. 

58.  What  is  the  sum  off,  3|,  and  i  off  ?        Ans.  4f££. 

59.  Add  -i-  of  a  £.  T\  of  a  s.  and  £  of  a  d.  together. 

Ans.  fH£- 

GO.     What  is  the  sum  of -J-  of  a  foot,  £  yd  £    rod,  J  fur.  £ 

mile;?  Ans. -f|i£=7  8119  2i  barley-corns. 

61.     Add  }  of  a  week.  £  day.  £  h.  ]  m.  and  f  sec.  together. 

Ans.  jfffii=2  6  45  12f  seconds. 


SUBTRACTION  OF  VULGAR  FRACTIONS. 

RULE.  Prepare  the  fractions  as  in  Addition,  and  the 
difference  of  the  numerators,  written  over  the  common  de- 
nominator, will  form  the  fraction  required. 

NOTE  1.  To  subtract  a  fraction  from  a  whole  number,  take  the 
numerator  from  the  denominator,  and  1  from  the  Avhole  number.  Ob- 
serve the  same  rule  in  mixt  numbers,  when  they  have  a  common  de- 
nominator. 

2.  When  the  lower  fraction  is  greater  than  the  upper,  sub- 
tract the  numerator  of  the  lower  fraction  from  the  denominator,  and 
fo  the  difference  add  the  upper  numerator,  carrying  1  to  the  whole 
number. 

EXAMPLES. 

62.  What  is  the  difference  between  f  and  f  ? 
5X8=40 

3X6=18 

22=diff.  of  the  numerators.  7  T.       ns—ii    A 
6x8=48=comniou  denominator.  J 

63.  What  is  the  difference  between  9|  and  f  of  6£  ? 

Ans.  7TV. 

64.  What  is  the  difference  between  f  of  6i  £.  and  |  of  a 
shilling  ?  Ans.  2f«£. 

65.  From  f  of  a  cwt.  take  f  of  an  oz.  An«. 

66.  What  is  the  difference  between  ^yd.  and  f  of  a  mile? 

Ans.  f|3». 

67.  From  a  year  take  f  of  an  hour.  Ans.  -f  f; 

68.  From  99  take  TV  Ans. 

69.  From  11|  Uke5f.  An- 

70.  From  98  f&  take  45  |f  .  Ans, 


VULGAR  FRACTIONS, 


MULTIPLICATION  OF  VULGAR  FRACTIONS. 

RULE.  Reduce  whole  or  mixt  numbers  to  improper 
fractions,  compound  fractions  to  simple  ones,  then  multiply 
the  numerators  into  each  other  for  the  numerator  of  the 
product,  their  denominators  into  each  other  for  the  denom- 
inator of  the  product. 

NOTE.  A  fraction  is  best  multiplied  by  an  integer  by  dividing  the 
numerator  by  it,  if  it  can  be,  otherwise,  multiply  the  denominator  by 
it.  Proof  by  Division. 

EXAMPLE;?. 
71.     Multiply  4  by  |. 

=f-  An8-*- 


72.  Multiply  12-&  by  67T7.  An*.  80Tf. 

73.  What  is  the  product  off  and  14  ?  Ans.  10|. 

74.  What  is  the  product  of  8  and  4  of  9  ?  Ans.  57| 


DIVISION  OF  VULGAR  FRACTIONS. 

RULE.     Prepare  the  fractions  as  in  multiplication  ;  then 
invert  the  divisor,  and  proceed  as  in  multiplication. 
PROOF.     By  multiplication. 

EXAMPLES. 

75.  Divide  f  by  £. 

5SXX43=!=»- 

76.  What  is  the  quotient  of  4  by  7  r  Ans.  ^. 

77.  Divide  8  by  4,  of  9.  Ans.  1£. 

78.  Divide  84  by  7-f.  Ans.  lTy¥. 

79.  Dividef  of  |  by  A  of  6  A.  Ans.  ^j. 

80.  Divide  8  by  12.  Ans.  f  . 

NOTE.  Multiplication  and  division  of  vulgar  fraction?,  as  in  ivhole 
nv.rnber.-,  muuia-'ly  prove  each  other.  That  the  rules  give  a  true  re- 
sult Vv''l]  appeal  evident  by  putting  <'«ny  two  whole  numbers  into  the 
form  of  fractions,  ai  ;iii  them  as  these  rules  direct, 

and    •  '1:6  rcvajt  oft  v.'iti:  lliiit  of  the  -:mc 

kind  ia  whole  numb* 


Qk  DECIMAL  FRACTIONS. 

PRACTICAL  QUESTIONS  IN  VULGAR  FRACTIONS. 

J.  AVhat  is  the  sum,  difference,  product  and  quotient  of 
-li  and  i?  ? 

Ans.  sum,  iy-°.  diff.  ^.  product,  |f|.  quotient  l^f 

2.  The  difference  of  two  numbers  is  1  |f ,  the  less  number 
2*- ;  what  is  the  greater  number  ?  Ans.  3f . 

3.  What  number  is  that,  which,  if  added  to  3f ,  will  give 
the  sum  8|f  ?  Ans.  4T7T. 

4.  What  is  f  of  130f  ?  Ans.  81|. 

5.  What  number  is  that,  which,  if  multiplied  by  a.  will 
produce  25|  P  Aus.  42J. 

6.  What  number  is  that,  which,  if  divided  by  %  will  be 
10-|  ?  Ans.  14. 


DECIMAL  FRACTIONS. 

~—3.  A  DECIMAL  is  the  tenth  part  of  an  unit. 

2.  If  1  lb.  or  yd.  was  divided  into  ten   equal  parts,  and 
each  of  these  parts  into  ten  other  equal  pans,  and  each  of 
these  again  into  ten  others,  and  so  on  in  a  ten-fold  propor- 
tion, without  end,  then  would  an  expression  of  any  num- 
ber of  these  parts  be  called  a  decimal  fraction. 

3.  The  denominator  of  a  decimal  fraction  is  always  1, 
with  as  many  ciphers  annexed  as  the  decimal  has  places. 
The  denominator  therefore,  being  known,  is  never  written, 
the  parts  being  distinguished  by  a  dot  prefixed,  called  the 
separatrijc,  or  decimal  point  ;  thus  .5=T%. 

4.  The  numerators   of  infinite  decimals  consist  of  the 
same  figure,  or  figures,  repeated  ;  and  their  denominators 
consist  of   as  many  nines  as  there  are  figures  in  the  repe- 


tend;  thus  G—  «-,  and 

5.  A  pure  decimal  is  when  the  fraction  is  proper  ;  as 

>5=A- 

6.  A  mixt  decimal  is  when  the  fraction  is  improper;  as 

19,45=^M,  or  19TW 

7.  When  the  denominator  is  an  even   part  of  the  nume- 
rator, increased  by  affixing  ciphers  to  it,  the  decimal  equal 
in  value  to  such  a  fraction  will  be/wite  aud  complete  :  as. 


DECIMAL  FRACTIONS.  Qj 

8.  But  if  the  denominator  is  no  even  part  of  the  nume- 
rator thus  increased,  the  decimal  equal  in  value  to  such  a 
fraction  will  be  infinite  ;  that  is,  it  will  constantly  repeat 
either  one  figure  only,  as  -f  =  ,666,  Sec.  ;  or  else  it  \vi!i  re- 
peat  a   certain   number   of  figures   perpetually,    as     4  = 

5714285  &c.  ;  and  T3f =,181 81 8  &c.  forever. 

9.  Those  decimals  which  constantly  repeat  or  circulate, 
are  called  repetends  or  circulates. 

10.  Those  decimals,  in  which  one  figure  only  repeats,  are 
called  a  single  repetend  ;  as  ,333  Sec. 

11.  Those,  in  which  several  figures  repeat,  are  called  a 
compound  repetend  :  as  ,185185  oce. 

12.  A  dot  is  placed  over  a  single  repetend,  and  over  the 
first  and  last  figure  of  a  compound  repetend,  for  the  greater 
perspicuity  in   the   operations  of  repeating  decimals  ;  as 

,3—18 — 185  &c. 

13.  In  a  compound  repetend,  any  one  of  the  circulating 
figures  may  be  made  the  first  of  the  repetend;  thus  in  the 

repetend  6,8395395395  &c.  it  may  be  made  6,83953  ;  or 

6,839539.  By  which  means  any  two  or  more  repetends 
may  be  made  to  begin  and  end  at  the  same  place  ;  and  ihen, 
they  are  said  to  be  similar  and  conterminous. 

14.  If  the  numerator  has  not  so  many  places  as  the  de- 
nominator   has    ciphers,   make   them  equal  by  prefixing 
ciphers  ;  thus,  TH  =  ,05  ;  7^¥=,007. 

15.  In  all  decimal  numbers,  if  the  decimal  point  be  re- 
moved one  place  towards  the  right  hand,  every  figure  will 
be  increased  in  a  ten-fold  proportion  ;  thus,  4,856 — 48.56 
— 485,C — 4856,  each  of  which  is  ten  times  of  greater  value 
than  the  one  preceding.     Consequently, 

16.  By  removing  the  decimal  point  one  place  towards  the 
left  hand,  the  value  will  be  decreased  in  a  ten-fold  propor- 
tion ;  thus,  4856,— 485,6—48,56— 4,856 — ,4856. 

17.  Ciphers,  placed   at  the  left   hand  of  decimals,  de- 
crease their  value  in   a  ten-fold   proportion,  by  removing 
them  further  from  the  decimal  point;  ,000005  =  J-Q-O O-TT<TO' 
or  5  parts  of  1000000. 

1 0.  Ciphers,  placed  at  the  right  hand  of  decimals,  neith- 
er increase  nor  decrease  their  value;  thus,  ,5  or  ,50,  or 
,5000  are  equal  to  .5=i. 

19.  All  decimals,  consisting  of  an  equal  number  of 
places  have  a  common  denominator  ;  and  decimals  of  une- 


66  DECIMAL  FRACTIONS. 

qual  denominators  are  reduced  to  a  common  denominator 
by  annexing  ciphers  til!  they  are  equal  in  places  :  thus,  ,6 
— ,06 — ,006.  may  be  reduced  to  the  (teeiimils  ,600 — ,060 — 
,006,  each  of  which  has  1000  for  a  common  denominator. 

TABLE  OF  NOTATION. 
Whole  Numbers.  Decimal  Parts. 


o 
a 

F 

20.  It  appears  from  the  table,  that  as  whole  numbers  in- 
crease in  a  tea-fold  proportion  towards  the  left  hand,  so  de- 
cimals decrease  in  a  ten-fold  proportion  towards  the  right 
hand. 

21.  The  place  of  tenths,  or  the  first  from  the  decimal 
point,  is  of  the  greatest  value  ;  therefore  that  decimal  is  of 
the  greatest  value  whose  highest  place  is  greatest,  without 
uny  regard  to  the  number  of  figures  ;    so  ,4  is  greater  in 
value  than  ,34788.     This  will  appear  evident  by  reducing 
them  both  to  a  common  denominator ;  thus,  400000  is  great- 
er than  34788. 

NOTE.  Decimal  Fractions,  being  the  same  in  their  nature  and 
od  of  operation  as  whole  numbers,  may  be  performed  >vith  the 
facility. 

ADDITION  OF  DECIMALS. 

CASE  I. 

To  add  finite  'decimals. 

RULE.     Place  the  numbers  under  each  other   according 
to  the  value  of  their  places  ;  add  them  as  in  whole  mi  in- 


DECIMAL  FRACTIONS.  Q^ 

berg,    set    the   decimal  point    as   many   places   from   the 
right  hand  as  are  equal  to  tS'e  greatest  number  of  decimal 
places  in  any  one  of  the  given  decimals. 
PROOF.     As  in  \vhob  numbers. 

EXAMPLES. 

1.  2.  3. 

83,845  38,45  1.074 

,80435  8,078  43'.8074 

3,0085  43.34  ,8U 

487,08  1,04  ,1007iU 

,3874  38,7454  9,000 

,0007  18,003  1,3471 

575,20595  Sums      147,6564  53,944-584 

In  example  first,  five  being  the  greatest  number  of  given 
decimals,  therefore  the  decimal  point  is  set  five  places 
from  the  right  hand. 

C4ASE    II. 

To  add  repeating  decimals,  when  there  is  a  single  repetend. 
RULE.  Make  thorn  conterminous,  that  is,  end  together, 
and  then  add  them  as  in  whole  numbers,  adding  to  the  last 
or  left  hand  place  of  decimals,  as  many  units  as  there  are 
nines  in  the  sum  5  the  last  figure  will  be  one  of  the  repe- 
tends. 

EXAMPLES. 

4.  Add  123,23— 63,516— 0,3'— 8.8— 4,83  and  18.016  to- 
gether. 

123,333 
63,516     tf: 

0,333     .1 

3 


8,800     £ 
4,833 
18,016 


218,833 


08  DECIMAL  FRACTIONS. 

n.  Add  8,342—8,8—3,1043  and  7,34  together. 
8,3422 
8,8888  | 
3,1043 


27,6798 

NOTE.     In  the  4th  example  the  sum  of  the  repetend?  is  21,  AvhK  u 
•es  two  nines,  therefore  2  i?   added  to  the  sum   of  the  repetends. 

The  sum  of  the  repetends  in    example  5,  being   17,  give.*;   one  nine, 

Therefore  1  is  added  to  the  sum  of  the  repetends. 

CASE  III. 

To  add  decimals  having  compound  repetends. 
RULE.  From  the  place  where  all  the  repetends  begin 
together,  continue  each  decimal  to  a  number  of  places 
equal  to  the  least  common  multiple  of  all  the  number  of 
figures  in  each  repetend;  then  add  as  before  directed,  and 
to  the  last  place  add  as  many  units  as  there  are  10's  in  the 
place  where  all  the  repetends  begin  together,  and  the 
figures  in  these  two  places  will  be  l\ie- first  and  last  of  the 
repetends. 

EXAMPLES. 

6.    Add    2,9543— 1,04— 3,7 — 4,065820    and    4,731    to- 

ther. 

Number  of  figures  in  each  repetend. 

'  4,3,2,6,4  2,954395433543 

1,041041041041 
3,737373737373 
4,065826065820 


gether. 


1,1,1.1,1  4,731473147314 

16,530109431099 

;;X2X2=12  least  com.  raultiple=to  the  number  of  places 
to  be  in  the  repetend. 

In  the  above  example  the  number  of  10's  where  the  repetends  be- 
gin i*  2,  therefore  2  is  added  to  the  last  place  or  right  hand  figure. 


DECIMAL  FRACTIONS.  gg 

SUBTRACTION  OF  DECIMALS. 

CASE  I. 

\ 

To  subtract  finite  decimals. 

RULE.  Place  the  numbers  according  to  their  value  ; 
subtract  as  in  whole  numbers,  and  point  off  for  decimals, 
as  in  Addition. 


EXAMPLES. 

1. 

2. 

From    793,74 

38,4567 

Take    324,73564 

8,2 

469,00436  30,2567  491,9926 

CASE  II. 

To  subtract  repeating  decimals  with  single  repetends. 
RULE.     Place  and  subtract  them  as    usual,  observing, 
when  the  subtrahend  is  the  greater  number,  to  increase  the 
upper  figure  by  9  only,  and  in  such  case  to  carry  1  to  the 
next  place. 

EXAMPLES. 
4.  5.  6. 

From    45,03333  34,5289  14,4516 

Take      9,84136  7,583  3  9,3ooe 

35,79196  26,9456  5,1516 

CASE  III. 

When  the  decimals  are  compound  repetends. 
RULE.  Prepare  them  as  directed  in  Case  II.  in  addi- 
tion ;  then  subtract,  observing  to  add  1  to  the  right  hand 
place  of  the  subtrahend,  if  one  is  borrowed  where  the  repe- 
tends begin  together ;  the  remainder  either  whole  or  in 
part  will  show  the  repetend. 

EXAMPLES. 

7. 

From   9,4i78     take  5,56. 

3,2 

3x2=6=multiple.  9,4178178  >  similar  and 

5,56565653  conterminous. 


3,8521612 


yO  DECIMAL  FRACTIONS. 

MULTIPLICATION  OF  DECIMALS. 
GENERAL  RULE. 

CASE  I. 

Place  the  numbers  under  each  other  without  any  regard 
to  their  value  ;  multiply  them  as  in  whole  numbers,  and, 
for  decimals,  point  off  from  the  right  hand  as  many  places 
in  the  product  as  there  are  decimal  places  in  both  the 
factors. 


EXAMPLES. 

Multiply 

by 

i. 

84,374 

8,5 

2. 
,347 
7,04 

1388 
24290 

2,44288 

421870 
674992 

717,1790 

CASE  II. 

33736 
59038 


,624116 


When  there  are  not  so  many  places  in  the  product  as  there 

are  decimals  in  the  two  factors. 

RULE.     Multiply  as  before,  and  make  up  the  deficiency 
by  prefixing  ciphers* 


4.  5.  6. 

5,72  3,347  ,34567 

,006  ,0008  ,0003 


903432  ,0026776  .,000103701 

CASE  III. 

To  multiply  any  decimal  by  10,  100,  1000,  &e. 
RULE.     Remove  the  decimal  point  in  the  multiplicand 
as  many  places  towards  the  right  hand  as  there  are  ciphers 
in  the  multiplier. 

7.  Multiply  ,8744  by  10,  100,  1000,  &c. 

Ans.  8,744 — 87,44—874,4. 

NOTE.     Any  number  multiplied  by  a  pure  decimal   is   diminished, 
;jbut  by  a  mixt,  it  is  increased. 


DECIMAL  FRACTIONS. 
CASE  IV. 


71 


When  the  multiplicand  has  a  single  repetend  and  the  multi- 
plier a  single  figure. 

RULE.  Multiply  as  usual,  ubserving  to  add  to  the  last 
place  in  the  product  as  many  units  as  it  contains  nines,  and 
that  place  will  be  a  repetend. 


EXAMPLES. 


Multiply 
by 


8. 

8,7016 
5 


43,5083 


9. 


34,444 


CASE  V, 

When  the  multiplier  consists  of  several  figures. 
RULE.  Multiply  as  before  directed,  making  each  partic- 
ular product  conterminous,  by  continuing  the  single  repe- 
tend of  each  towards  the  right  hand. 


EXAMPLES. 


10. 


Multiply  234,64 
by      ,634 

93857 

703933 

14078666 


148,76457 


11. 

84,36 
,425 

42183 

16873s 

33746c  G 

35,85583 


CASE  VI. 

When  the  multiplier  is  a  repetend. 

RULE.  Multiply  as  usual;  add  a  cipher  to  the  product, 
or  which  is  the  same,  cut  off  one  decimal  less  than  usual, 
and  divide  by  9,  continuing  the  quotient  till  it  becomes  a 
single  or  compound  repetend,  which  will  be  the  answer. 


DECIMAL  FRACTIONS, 


EXAMPLES. 

12.                                      13.  14. 

Multiply  8,35                              712,54  37,23 

by      ,04              .                      ,03  ,26 

9)3,340                        9)213,763  9)22,340 

j37i=true  product.  23,751*48  2482 

7446 


9,928 
CASE  VII, 

When  the  multiplicand  is  a  compound  repetend,  and  the 
multiplier  a  single  figure  only. 

RULE.  Multiply  as  in  whole  numbers,  observing  to  add 
to  the  right  hand  place  of  the  product  as  many  units  as 
there  are  tens  in  the  product  of  the  left  hand  place  of  the 
repetend.  The  product  will  contain  a  repetend  whost 
places  are  equal  to  those  in  the  multiplicand. 

EXAMPLES. 

15.  16.  17. 

Multiply  582,347  924,378  3749,23 

by  8  ,03  ,007 

4658,778  27,73135  26,24464 


CASE  VIII. 

When  the  multiplier  consists  of  several  figures. 

RULE.  Multiply  as  before,  making  each  particular  pro- 
duct conterminous  towards  the  right  hand. 


DECIMAL  FRACTIONS.  73 

EXAMPLES. 
18.  19. 

Multiply  873,2586  8427.3012 

by  43,7  4370,2 

61128106  168546025 

26197759?  58991 1089n 

349303^634  2528 i 9038i9o 

3370920509205 


38161,40338 


36828992,02332 


CASE  IX. 


When  the  multiplier  is  a  compound  repetend. 
RULE.  Multiply  each  figure  in  the  repetend,  as  in  whole 
numbers,  and  add  the  several  products  together;  then  add 
the  result  to  itself  by  placing  the  first  left  hand  figure  so 
many  places  forward  as  exceeds  the  number  of  places  in 
the  repetend  by  one,  and  the  rest  of  the  figures  in  order 
after  it;  proceed  thus  till  the  result  last  added  be  carried 
beyond  the  first  result ;  add  these  several  results  together, 
heginning  under  the  right  hand  place  of  the  first,  and  from 
that  place  point  off  with  a  dot  as  many  figures  for  a  repe- 
tend as  there  are  figures  in  the  repetend  of  the  multiplier, 

EXAMPLES. 

20.  21. 

Multiply  1235,01  42710,36 

by         3,26  ,20403 

741006  12813108 

247002  17084144 

370503  8542072 


First  result.     4026.1326          8714,1947508  first  result, 
'40261326  87141975 

4026  &c.  871  &c. 


True  product  4030,1627         8714,2818936 


y-j,  DECIMAL  FRACTIONS. 

CASE  X. 
When  the  multiplicand  and  multiplier  both  are  compound 

repetends. 

RULE.  The  places  of  the  repetend  in  the  product  will  be 
uncertain  as  to  their  number, -and  can  only  be  determined 
by  continuing  and  repeating  the  first  product,  which  will 
contain  a  certain  repetend.,  being  equal  in  places  to  those  of 
the  multiplicand. 

NOTE.  If  the  finite  figures,  (that  is  the  figures  preceding  the  repe- 
tend) are  few,  and  the  places  of  the  repetend  many,  the  work  may 
he  shortened  by  subtracting  the  finite  figures  from  those  of  the  repe- 
tend, whidh  will  give  a  new  multiplier. 

EXAMPLES. 

22. 

Multiply  3,145  4,297 

by  4,297  4=finitepart. 

4,293=new  multiplier. 
3.145 
4,293 

9436 

28309o 

62909  o 

12581318 


JFirst  product  1350343636 3 6  &c. 

13503436s  &e. 

135034  &e. 

135  &c. 


True  product  13,5169533 

DIVISION  OF  DECIMALS. 

CASE  I. 

RULE.  Place  the  numbers  and  divide  them  as  in  whole 
Burnbers,  and  point  off,  at  the  right  hand,  for  decimals,  us 
many  places  as  the  decimal  places  in  the  dividend  exceed 
those  in  the  divisor. 


DECIMAL  FRACTIONS,  y^ 

OBSERVATION  1.  If  after  dividing  there  should  not  be  so  many 
places  in  the  quotient  and  divisor  together  as  there  are  in  the  divi- 
dend, make  them  equal  by  prefixing  ciphers  to  the  quotient. 

2.  The  quotient  figure  is  always  of  the  same  value  with  that  figure 
of  the  dividend,  under  which  the  unit's  place  of  its  product  stand*.  Or, 

3.  The  decimals  in  the  quotient  and  divisor  added  together  must 
always  be  equal  in  number  with  those  in  the  dividend. 

4.  When  the  decimal  places  in  the   divisor  and  dividend  are  equal 
in  number,  the  quotient  will  be  whole  numbers. 

5.  When  the  decimals  in  the  dividend  exceed  those  in  the  divisor^ 
the  decimals  in  the  quotient  must  be  equal  to  that  excess. 

6.  If  the  decimals  in  the  divisor  exceed  those  in  the  dividend,  they 
must  be  made  equal  by  annexing  ciphers  to  the  dividend  ;  and  then 
all  the  figures  in  the  quotient  will   be   whole   numbers,  till  all   the 
ciphers  annexed  are  used. 

7.  When  there  is  a  remainder  after  division,  ciphers  may  be  an- 
nexed to  the  dividend,  and  the  work  prolonged  at  pleasure,   and  in 
such  cases  the  quotient  will  be  decimals. 

In  division  of  decimals,  there  may  occur  nine  varieties, 
with  respect  to  the  nature  of  the  three  sorts  of  numbers  ; 
viz. 

1.  Integers,  or  whole  numbers. 

2.  Mixt  numbers,  that  is,  integers  and  decimals. 

3.  Pure  decimals,  that  is,  without  any  whole  numbers. 
*fhe  dividend,  therefore,  being  itself  of  three  kinds,  and 
capable  of  a  divisor  of  three  kinds,  there  may  arise  nine 
varieties,  viz. 

Whole  number. 


1.  A  whole  number  may  be  divided  by  a 


2,  A  mixt  number  may  be  divided  by  a 


3.  A  pure  decimal  may  be  divided  by  a 


Mixt  number. 
Decimal. 
Whole  number. 
Mixt  number. 
Decimal. 
Whole  number. 
Mixt  number. 


Decimal. 

The  various  cases  more  fully  explained  by  the  subse- 
quent operations  at  large,  will,  with  attention  to  the  prece- 
ing  observations,  render  Division  of  Decimals  sufficiently 
easy  and  plain. 

The  whole1  may  be  exemplified  in  this  simple  example  ; 
Let  looG  be  divided  by  12. 

First  variety.         12)1866,0 

155,5  (By  obs.  7  and  5.) 


DECIMAL  FRACTIONS. 


In  variety  first  the  divisor  and  dividend  are  both  whole  numbers, 
and  because  there  was  a  remainder  of  6  a  cipher  is  annexed  to  the 
dividend  (obs.  7.)  which  gives  one  decimal  figure  in  the  quotient 
(obs.  5.) 


Variety  2d. 
Variety  3d. 
Variety  4th. 
Variety  5th. 
Variety  6th. 


12)186,60 

15,55  (By  obs.  5.) 
12),18660 


,01555  (By  obs.  1.) 
1,2)1866,0 

1555  (By  obs.  4  and  6.) 

1,2)186,60 

155,5  (By  obs.  3  and  5.) 

1,2),18660 

,1555  (By  obs.  3.) 


Variety  7th.     ,12)1866,00 

15550  (By  obs.  4  and  6.) 
Variety  8th.      ,12)18,660 

155,5  (By  obs.  5.) 
Variety  9th.       ,12),18660 

1,555  (By  obs.  5.) 

The  following  examples  will  further  illustrate  the  gen- 
eral rule,  and  more  clearly  exemplify  the  preceding  obser- 
vations. 

10.  Divide  295,75  by  8,45. 

295*75-j-8,45=:35  Ans. 

11.  Divide  ,4884  by  ,0074. 

4884-r-,0074==66  Ans. 

NOTE  1.  In  examples  10  and  11,  the  decimals  in  the  divisor  and 
dividend  are  equal,  the  quotients,  therefore,  in  both  instances  are 
whole  numbers.  See  obs.  4. 

12.  Divide  780.516  by  24,3. 

780,516—24,3=32,12  Ans. 

13.  Divide  ,3953  by  ,67. 

?3953-r-?67=?59  Aps, 


DECIMAL  FRACTIONS.  yy 

2.  In  examples  12  and  13,  the  decimal  places  in  the  dividend  ex- 
ceed those  in  the  divisor  by  2  figures  ;  therefore  two  figures  are  point- 
ed off  for  decimals  in  the  quotient.     See  obs.  5. 

14;  Divide  192,1  by  7,684. 

192,1-7,684=25  Ans. 

15.  Divide  441. by  ,7875 

,7875)441.0000(560  Ans.. 
39375 

47250 
47250 

00 

3.  In  examples  14  and  15.  the  decimal  places  in  the  dividend  are 
not  so  many  as  those  in  the  divisor  by  3  and  4,  therefore  ciphers  are 
annexed  (See  obs.  6.)  to  make  them  equal ;  and  the  quotient  is  whole 
numbers.     See  observation  4. 

16.  Divide  7,25406  by  957. 

7,25406-r-957=,00758  Ans. 

17.  Divide  ,0007475  by  ,575. 

,0007475-f-,575=,0013  Ans. 

4.  In  examples  16  and   17,  after  the  division  was  finished  there 
were  not  so  many  places  in  the  quotient  and  divisor  added  together, 
as  there  were  in  the  dividend  ;  therefore,  they  are  made  equal  by 
prefixing  2  ciphers  to  the  quotient.      See  obs.  1. 

CASE  II. 

To  divide  any  whole,  mixt,  or  decimal  number  by  10,  100, 

1000,  &c. 

RULE      Remove  the  decimal  point  towards  the  left  hand 
so  many  places,  as  there  are  ciphers  in  the  divisor. 

EXAMPLES. 

1.  Divide  1866  by  10,  100.  1000,  &e. 
Ans.  10)186,6         100)18,66         1000)1,866  &c. 

CASE  111. 

When  the  dividend  has  a  single  repetend  and  the  divisor 

a  single  finite  figure. 

RULE.     Divide    :.s   usual,    and   when   the  repetend   is 
brought  down  the  quotient  will  begin  to  repeat. 


yg  DECIMAL  FRACTIONS, 

EXAMPLES. 

2.  Divide  734,02  by  8.  3.  Divide  3184,6  by  ,6. 

8)734,02  ,6)3184,6 

91,77  perpetual  repeteud.         5306  perpetual  repetend. 

CASE  IV. 

When  the  divisor  contains  a  number  of  finite  figures. 
RULE.     Divide  as  usual,  and  the  quotient  will  repeat  a 
single  figure,  but  will  not  always  begin  when  the  repetend 
is  brought  down. 

EXAMPLES. 

4.  Divide  79,26  by,48.    5.  Divide  1 06036,783  by  487,65. 

,48)79,26(165,138  487,65)106036,783(217,4 

48  97530 

312  85067 

288  48765 

246  363028 

240  341355 

66  216733  C  perpetual 

48  195060  \  repetend. 

186  21673 

144 

426    C  perpetual 
384    I  repetend. 

42 

CASE  V. 
When  the  divisor  is  a  single  repetend  and  the  dividend  a 

finite  number. 

RULE.  Multiply  the  dividend  by  9,  cut  off  from  the 
right  hand  of  the  product  one  figure  more  than  usual  (this 
being  the  same  as  dividing  by  10)  for  a  new  dividend; 
then  divide  the  new  dividend  as  usual,  and  the  quotient 
will  be  the  answer.  Or  place  the  given  dividend  under 
itself,  but  one  place  forward  towards  the  right  hand,  and 
subtract  5  the  remainder  will  be  the  new  dividend. 


DECIMAL  FRACTIONS.  yg 

EXAMPLES, 
6.  Divide  572,4  by  ,8.  Or,  572,4 

9  5724  a  figure  forward. 

,8)515,16  =  newdivid'd.  ,8)515,16  as  before. 

643,95  Ans.  643,95  Ans. 

CASE  VI. 
When  the  divisor  consists  of  finite  numbers  joined  to  the 

repetend,  and  the  dividend  is  finite. 

RULE.  Subtract  the  finite  numbers  of  the  divisor  from 
the  divisor  itself*  and  the  .remainder  will  be  a  new  diviser, 
then  prepare  the  dividend  as  in  Case  V.  for  a  new  divi- 
dend which  divide  as  usual. 

EXAMPLES. 

7.  Divide  8569,88  by  4,86*. 

From  4,86  From  8569,88 

Take      48 =finite  number.  Take     856988 

4.38=new  divisor.  7712,892=new  dividend. 

Then  7712,892-4-4,38  =1760,9  Ans. 

CASE  VII. 

When  there  is  a  repetend  both  in  the  divisor  and  dividend. 
RULE.     Prepare  them  as  before  directed  in  Cases  V.  and 
VI,  then  divide  and  the  quotient  will  be  either  finite,  a  sin- 
gle, or  a  compound  repetend. 

EXAMPLES. 

8.  Divide  234,6  by  7.     9.  Divide  134,26  by  ,6. 

From  234,6e  From  134,266 

Take     2346  13426 


7)21  l,20=new  dividend.    ,6)120,84  =^new  dividend, 

30,1 714285= Ans.  201,4= Ans. 

CASE  VIII. 
When  the  divisor  or  dividend,  or  both  contain  compound 

repetends. 

RULE.  Set  the  divisor  and  dividend  under  themselves 
so  many  places  forwards  to  the  right  hand,  ;is  there  are 
places  in  the  repetend  of  the  divisor  exclusively  ;  subtract 
them  and  the  remainders  will  be  respectively  a  new  divisor 
and  dividend. 


80  DECIMAL  FRACTIONS. 

EXAMPLES. 
10.  Divide  243,306  by  11 1,98. 


From  243,306 
243 


111,98 
11 


243,063=new  dividend.       lll,87=new  divisor. 
111,87)243,063(2,172  Am. 

NOTE  1.     If  there  is  no  finite  part  in  the  divisor,  no  subtraction 
must  be  made  from  it. 

11.  Divide  395,273614  by  ,317. 
395,273614 
395273 


,317)394,878341(1245,673  Ans. 

2.  If  there  is  norepetend  in  the  divisor,  whatever  the  dividend 
may  be,  no  subtraction  is  to  be  made  either  in  the  divisor,  or  divi- 
dend. 

12.  Divide  319,28007*112  by  764,5. 

764,5)319,280071 12(,4176375  Ans. 
30580 


13480 
7645 

58350 
53515 

48357 
45870 

24871 
22935 


19361 
15290 

40712 
38225 

2487     J 


Perpetual  repetend 


DECIMAL  FRACTIONS.  g[ 

Xo  IP. .  1 .  A  series  of  nines,  infinitely  continued,  is  equal  to  unity* 
or  one.  in  the  next  left  hand  place  ;  thus,  0,999  &c.  is  equal  to  1  : 
and  ,0999  &c.=,l  ;  and  ,00999  £c.=,01 ;  and  54,999  &c.=55. 

DEMONSTRATION.  It  is  obvious  that  ,9=yk  wants  only  TV  of 
unity,  and  ,99  wants  only  T£7,  ,999  wants  only  y  oV  ¥5  of  unity  ; 
so  that  if  the  series  were  continued  to  infinity,  the  difference  between 
that  series  of  nines  and  an  unit,  would  be  equal  to  unity  divided  by 
infinity,  that  is,  nothing. 

2.  A  single  repetend  multiplied  by  10,  and  then  subtracted  from 
that  product,  the  remainder  will  be  the  same  number,  made  finite,  in 
the  next  superior  place  ;  thus  ,6666    &c.    multiplied  by   10  will  be 
equal  to  6,666  Sec.  ;   from  which  subtract  ,666  &c.    there   will  re- 
main 6  a  whole  number  ;  as  6,666  &c.  ; 

666  &c.  ; 

6   •  •  *=whole  number. 

3.  If,  therefore,  a  compound  repetend  be  multiplied  by  an  unit  with 
as  many  ciphers  annexed  as  are  equal  to  the  number  of  places  in  the 
repetend,  and  then  subtracted  from  that  product,  there  will  remain 
at  the  left  hand  the  same  numbers  made  finite  Avhich  made  the  repe- 
tend ;  thus    325  multiplied  by   1000=325,325  from  which  if  ,325  be 
subtracted,  there  will  remain  325  made  finite. 

4.  If  any  repetend  be  multiplied  by  so  many  nines  as  it  contains 
places,  the  result  will  be  the   repetend  made  finite,  for  any  number 
multiplied  by  10  and  once  subtracted  is  the  same  as  multiplied  by  9  ; 

thus  ,666  &c.  X9=5,999  &c.=6.   by  note   1.       And    527X    999= 
526,999=527.  by  note  1. 

REDUCTION  OF  DECIMALS. 
CASE  I. 

fo  reduce  a  vulgar  fraction  to  its  equivalent  decimal. 
RULE.     Divide  the  numerator  with  ciphers  annexed,  by 
the  denominator,  the  quotient  will  be  the  decimal. 

EXAMPLES. 

1.  Reduce  |,  |  and  f  to  decimals. 

4)1,00  2)1,0  4)3,00 

,25  Ans.  ,5  Ans.  ,75  Ans. 

2.  Reduce  fi  to  a  decimal,  Ans.  ,916. 

NOTE.  A  whole  number  may  be  expressed  decimally  by  annexing 
ciphers  and  the  decimal  point ;  thus,  874=874,000  &c. 

8 


$2  DECIMAL  FRACTIONS. 

CASE  II. 

To  reduce  coins,  weights,  measures  and  time  to  decimal 

fractions. 

RULE.  Place  the  numbers  perpendicularly  under  each 
other,  beginning  with  the  lowest  denomination,  and,  after 
annexing  ciphers,  divide  it  by  so  many  as  make  one  of"  the 
next  higher  denomination,  as  in  Reduction  Ascending  ; 
continue  thus  to  divide  till  it  is  reduced  as  high  as  the 
question  requires  ;  the  last  quotient  will  be  the  decimal. 

EXAMPLES. 

3.  Reduce  12  8£  qrs.  to  the  decimal  of  a  £. 

4)2,0 

12)850 
20)127083 

,635416£.  Ans.  ,635416£. 

4.  Reduce  4s.  to  the  decimal  of  a  guinea.    Ans.  ,142857. 

5.  Reduce  7   13  pwt.  to  the  decimal  of  a  pound  Troy. 

Ans.  ,6375. 

6.  Reduce  4213  Ib.  to  the  decimal  of  a  ton. 

Ans.  ,230803571428. 

7.  Reduce  3  14  Ib.  to  the  decimal  of  cwt.        Ans.  ,875. 

8.  Reduce  412  inches  to  the  decimal  of  a  mile. 

Ans.  ,00249368. 

9.  Reduce  52  days  to  the  decimal  of  a  year. 

Ans.  ,142465753. 

10.  Reduce  3  18  14  18  seconds  to  the  decimal  of  a  year. 

Ans.  ,01030117960426. 

CASE  III. 

r£o  reduce  shillings,  pence  and  farthings  to  decimals  by 

inspection. 

RULE.  To  half  the  greatest  even  number  of  shillings, 
add  the  farthings  contained  in  the  given  pence  and  far- 
things, increasing  the  second  decimal  place  by  5,  when  the 
shillings  are  odd,  and  the  third  place  by  1  when  the  far- 
thiiigs  exceed  12,  and  by  2  when  they  are  more  than  35  : 
the  three  places  will  be  the  decimal. 


DECIMAL  FRACTIONS.  33 


EXAMPLE. 

11.  Reduce  12  8£  qrs.  to  the  decimal  of  a  pound. 
6     =half  the  greatest  even  number  of  shillings* 
34=farthings  in  the  given  pence  and  farthings. 
l=excess  of  12. 

,635=deeimal  of  a  £.  Ans.  ,635  «£. 

NOTE.  If  the  second  and  third  places  of  the  decimal  are  25,  50,  or 
75,  the  decimal  is  finite  and  complete  ;  but  if  not,  more  figures  may 
be  found  by  the  following, 

RULE.  If  the  second  and  third  figures  are  under  25,  multiply  them 
by  4,  and  for  every  24  add  1  to  the  product,  and  the  result  will  be 
more  places  which  may  be  annexed  to  the  former  number.  If  the 
second  and  third  places  are  more  than  25,  multiply  the  excess  of  25, 
50,  or  75  by  4,  adding  1  for  every  24,  and  so  on  till  the  decimal  be- 
comes finite  or  infinite. 

EXAMPLE. 

12.  Reduce  12  8£  qrs.  to  the  decimal  of  a  £. 
6  =half  even  shillings.  More  figures  than  Hint?.- 

34=farthings  in  8£.  10=excess  of  25. 

l==excess  of  12.  4 

635=decimal  of  a  £.  40 

l=24*s  in  40. 

63541  41=t\vo  more  figures. 

16=excess  of  25. 
4 

635416  64 

2=24's  in  64. 

66=tvvo  more  figures. 
,635416  Ans. 

NOTE.  Half  the  even  number  of  shillings,  with  the  decimal 
point  prefixed  is  their  decimal,  and  when  the  shillings  are  odd,  a  ci- 
pher annexed  arid  divided  by  2,  the  quotient  will  be  the  decimal. 

13.  Reduce  1,   2,  3,     4,    5,    6,   7,  shillings  to  decimals, 
\nswers  ,05-,l-,15-,2-,25-,3-,35. 


§4  DECIMAL  FRACTIONS. 

CASE  IV. 

To  find  the  value  of  a  decimal. 

RULE.  Multiply  the  given  decimal  by  so  many  of  the 
next  less  denomination  as  make  one  of  the  same  with  the 
given  decimal,  as  in  Reduction  Descending,  and  cut  oft*  from 
the  right  hand  of  the  product,  as  many  places  for  decimals, 
as  there  are  decimals  in  the  given  fraction  ;  in  this  manner 
proceed  till  the  decimal  is  reduced  to  the  lowest  denomina* 
tion,  each  time  cutting  off  as  before  ;  the  several  denomi- 
nations on  the  left  hand  will  be  the  answer. 

EXAMPLES. 

14.  What  is  the  value  of  ,635416  of  a  £  ? 

20 


12,70833 
12 

£,50000 
4 

2,0000  Ans.  12  8|  qraf1. 

15.  What  is  the  value  of  ,142857  of  a  guinea  ? 

Ans.  4s. 

16.  What  is  the  value  of  ,6375  of  a  Ib.  Troy  ? 

Ans.  7  13  pwt. 

17.  What  is  the  value  of  ,230803571428  of  a  ton  ? 

Aus  4  2  13  Ib. 

18.  What  is  the  value  of  ,875  of  a  cwt  ?     Ans.  3  14  Ib. 

19.  What  is  the  value  of  ,00249368  of  a  mile  ? 

Ans.  4  1  2  in. 

20.  What  is  the  value  of  ,142465753  of  a  year  ? 

Ans.  52  days. 

21.  What  is  the  value  of  ,01030117960426  of  a  year  ? 

Ans.  3  18   14  18  seconds. 

CASE  V. 

To  find  the  value  of  any  decimal  of  a  pound  by  inspection. 
RULE.     Double  the   first   decimal   figure   for  shillings, 
adding  one   when  the  second  figure  is  more  than  4  ;  call 


DECIMAL  FRACTIONS.  85 

the  figures  in  the  second  and  third  places,  after  deducting 
5,  <o  many  farthings,  abating  one  vvheu  they  exceed  12 
and  two  when  they  exceed  35. 

EXAMPLES. 

22.  Find  by  inspection  ,635  of  a  £. 
s.  12=<louljle  tbe  first  decimal. 

8  &=  farthings  in  2d  and  3d  decimals, 

abating  for  excess  of  35. 

12  8^  qrs.  Ans.  12  8  £  qrs. 

23.  Find  by  inspection  the  value  of  ,038  of  a  £. 

Ans.  9rf. 

24.  Find  by  inspection  the  value  of  ,004  of  a  £,. 

Ans.  Id. 

CASE  VI. 

To  reduce  any  finite  or  pure  infinite  decimal  to  its  primitive 

vulgar  fraction. 

RULE.  Reduce  the  fraction  to  its  lowest  terms,  and  it 
will  form  the  fraction  required. 

NOTE.  The  denominator  of  a  finite  fraction  is  an  unit,  with  as 
many  ciphers  annexed  as  there  are  figures  in  the  decimal  ;  and  the 
denominator  of  an  infinite  decimal  is  as  many  nines  as  there  are  figures 
in  the  repetend. 

EXAMPLES. 

25.  Reduce  ,25  to  its  primitive  vulgar  fraction. 
25)TVo  =*• 

26    Reduce  ,6  to  a  vulgar  fraction. 

3)f =| •  m    .  Ans.  f. 

27.  Reduce  ,345  to  a  vulgar  fraction.  Ans.  |if. 

CASE  VII. 

To  reduce  a  mixt  decimal  to  its  primitive  vulgar  fraction. 
RULE.     Reduceutlie  finite  and  circulating  parts,  each  to 
a  vulgar  fraction,  separately  ;  add  them  together,  and  their 
sum  will  be  the  fraction  required. 

NOTE.  1.  The  finite  part  of  a  fraction  is  the  figures,  which  precede 
the  repetend,  and  has  always  10,  100,  &c.  for  its  denominator  ;  the 
circulating  part  is  the  repetend,  whose  denominator  is  always  9, 
99,  &c. 

8* 


gg  DECIMAL  FRACTIONS. 

2.  If  the  given  repetend  has  one  or  more  cipher-;  prefixed,  or  is  one 
or  more  places  from  the  decimal  point,  so  many  ciphers  mast  be  an- 
nexed to  the  denominator  ;  and  it'  the  repetend  includes  a  "whole 
number,  as  many  ciphers  must  be  annexed  to  the  numerator  as  that 
number  contains  figures. 

EXAMPLES. 

28.  What  is  the  primitive  vulgar  fraction  of  ,16  ? 
TV=finite  part,     /^circulating  part. 

90  J 
ToX/o=  60  \  numerators. 

150=sum  nume.  Jjj-o=£'  Ans.  £.. 

10x90=900=com.  denom. 

29.  Reduce  ,0047  to  a  vulgar  fraction. 
ToVo  =nnite  part.  ¥¥\7  circulating  part. 

TOOO  ^ 

TuVoXinfVo  =360005    Iiamerator«      <rf  iHHHnr=ir£!0  Ans. 

43000=suni  nnmer. 
1000x9000r=9000000=commoa  denora. 

30.  Reduce  31,62  to  a  vulgar  fraction. 

Tn  "> 

numerators'  3° 


31590=sum  of  numerators. 
lX999=999=com.  denominator. 

31.    Reduce  ,138  to  a  vulgar  fraction.  Ans.  -3^. 

CASE  VIII. 

To  make  fractions  similar  and  conterminous,  that  is,  to  be- 
gin and  end  at  the  same  place. 

RULE.  1.  Find  the  least  common  multiple  of  the  several 
numbers  of  places  in  each  repetend  of  the  given  decimals. 

2,  Make  the  new  repetend  equal  in  number  with  the  least 
common  multiple,  already  found,  beginning  the  repetend  as 
many  places  from  the  decimal  point  as  are  equal  to  the 
greatest  given  number  of  finite  places,  or  where  the  finite 
part  ends. 


FEDERAL  MOSEY. 


EXAMPLE. 

32.  Make  the   following  repetends   similar   and  conter- 
minous. 
Unequal. 

,6  2)2  6  ,6GG6666eT 

,045  13X2     6  least  com.  mul-     >04545454 

tiple  of  the  sev- 
eral given  repe- 


,027 
,025 

,112857 


tends. 


,02777777  J-  |  g 
,02500000 


FEDERAL  MONEY. 


1.  By  an  act  of  the  government  of  the  United  States,  accounts- 
must   be   kept    in    dollars,   dimes,     cents,    and  mills.      These    de- 
nominations perfectly  correspond  in  their  nature  with  decimal  frac-r 
tions,  increasing  and  decreasing  in  tenfold  proportion.     The  method 
of  operation,  therefore,  is  the  same  as  decimal  fraction?,    or  whole 
numbers. 

2.  By  an  act  of  Congress  it  was  resolved,  that  there  should  be 

Pure.  Standard. 


Two  Gold  (1.  The  Eatfe      .     =$10     weighing  247,5  grs. 
coins  ;  viz.    {  2.  The  half  Eagle  .     =5                   123,75 
f  1.  The  Dollar  .     .     =1                   371,25 
2.  Half  Dollar  .     .      =,50  cents.  185,625 
Six  Silver    j  3.  Quarter  Dollar  •      =,25             92.8125 
coins;  \\zA  4.  Double  Dime    .       =,20                 74,25 
j  5.  Dime       .     .     .      =,10               37,125 
LG.  Half  Dime  .     .      =,05              18,5625 
2  Copper   <  1.  The  Cent     .     .      =,10  mills.          208 
coins  ;  viz.  (  2.  The  half  Cent  .     .  =,5  mills.           104 

270  grs. 
135 
416 
208 
104 
83,2 
41,6 
20,8 
208 
104 

Any  sum  in  federal  money  may  be  read  either  in  the  lowest  denom- 
ination, or  partly  in  the  higher,  and  partly  in  the  lowest  ;  thus, 
$54,321  may  be  read  54321  mills,  or  5432  cents  1  mill,  or  543  dimes 
2  cents  1  mill,  or  5  eagles  4  dollars  3  dimes  2  cents  1  mill  ;  all  which 
denominations  may  be  easily  distinguished  by  the  decimal  point,  thus 
JE.:/.  dot-  di.  cent  mill, 
5,4,  3,2  ,  1. 

The  method  best  adapted  to  practical  purposes,  and  which  has  been 
sanctioned  by  a  law  of  the  United  States,  is  the  decimal  form  of  expres- 
sion by  a  decimal  point,  making  the  dollar  the  money  unit.  Dollars, 
therefore,  will  occupy  the  place  of  units,  and  the  less  denominations 
will  be  decimal  parts  of  a  dollar  and  distinguished  by  the  decimal 
point. 


Qg  FEDERAL  MONEY. 

The  established  custom  is  to  read  them  in  dollars  cents  and  mills  ; 
thus,  $54,32,1. 

NOTE.     Some  accountants  omit  the  decimal  point,  keeping  the 
several  denominations  distinctly  apart. 

REDUCTION  OF  FEDERAL  MONEY. 

CASE  I. 

To  change,  dollars  into  cents. 
RULE.     Add  two  ciphers. 

EXAMPLE. 

1.  In  §89  how  many  cents  ?  Ans.  8900  c. 

CASE  II. 

To  change  dollars  into  mills. 
RULE.     Add  three  ciphers. 

EXAMPLE. 

2.  In  $79  how  many  mills  ?  Ans.  79000  m. 

CASE  III. 

To  change  mills  to  dollars  and  cents. 
RULE.     Cut  oft'  the   three   right   hand  figures,  the   left 
hand  figures  will  be  dollars,  the  two  first  figures  on  the 
right  hand  will  be  cents  and  the  third  mills. 

EXAMPLE. 

3.  In  8748  mills  how  many  dollars  and  cents  ? 

88,748=g8,74,8  *  Ans.  $8,74,8. 

CASE  IV. 

To  reduce  cents  to  dollars. 

RULE.     Cut  off  t!»e  two  right  hand  figures  for  cents,  the 
left  hand  figures  will  be  dollars. 

EXAMPLE. 

4.  Reduce  74874  cents  to  dollars.  Ans.  $748,74. 

CASE  V. 

To  change  pounds  to  dollars, 
Add  a  cipher  and  divide  by  3. 


FEDERAL  MONEY.  gg 

EXAMPLES. 

£  Reduce  £36  to  dollars. 

3)360 

$120  Ans.  $120. 

$.  la  £225  how  many  dollars  ?  Ans.  $750. 

CASE  VI. 

To  reduce  pounds  and  shillings  to  dollars,  cents  and  mills. 
RULE  To  the  pounds  annex  half  the  greatest  even 
number  of  shilling,  to  which  annex  three  ciphers  if  the 
shillings  are  even  ;  but  if  the  shillings  are  odd,  to  the 
pounds  annex  a  5  and  two  ciphers  ;  divide  by  3,  cut  off 
three  right  hand  figures  for  cents  and  mills,  the  left  hand 
figures  will  be  dollars.  » 

EXAMPLES. 

7.  In  £44  16  how  many  dollars,  cents  and  mills  ? 
44=pounds. 

8=haif  the  greatest  even  number  of  shillings-, 

000 


3)448000 

$149,33,3|.  Ans.  g!49,33,3i. 

8.  Reduce  £74  15  to  dollars,  cents  and  mills. 

3)747500 

$249,16,6-|  Ans.  $249,  16,6|. 

CASE  VIL 

To  reduce  pounds,  shillings,  pence  and  farthings  to  dollars, 

cents  and  mills. 

RULE.  For  the  shillings  proceed  as  in  Case  VI.  to 
which  add  the  farthings  contained  in  the  given  pence  and 
farthings,  increasing  their  number  by  1  when  they  exceed 
12,  by  2  when  they  are  more  than  35,  to  which  annex  one 
cipher;  divide  the  whole  by  three,  and  cut  off  three  right 
hand  figures  for  cents  and  mills,  the  left  Land  figures  will1 
be  dollars. 


90  FEDERAL  MONEY. 

EXAMPLES. 

9.  In  £34  18  9£  how  many  dollars,  cents  arid  mills  ? 

3)349400 

$116,46,Gf  Ans.  $116,46,6f. 

10.  In  £93  11  4£  how  many  dollars  and  cents  ? 

Ans.  $311   90. 
CASE  VIII. 

To  reduce  dollars  to  pounds  and  shillings. 
RULE.     Multiply  the  dollars  hy  3,  doubling  the  right 
Land  figure  for  shillings. 

EXAMPLES. 

11.  In  g!28  how  many  pounds  and  shillings  ? 

* 


£38  8  Ans.  £38  8. 

12.  In  $74  how  many  pounds  and  shillings  P 

Ans.  £22  4. 
CASE  IX. 

To  change  dollars  and  cents  to  pounds,  shillings,  fyc. 
RULE.  Multiply  the  dollars  and  cents  by  3,  and  cut  off 
three  right  hand  figures  ;  the  figures  on  the  left  hand  will 
he  pounds,  and  those  on  the  right  decimals  of  a  pound, 
which  being  multiplied  by  20,  12  and  4,  (as  in  Case  IV. 
Reduction  of  Decimals,)  each  time  cutting  off  the  three 
right  hand  figures,  will  give  the  answer  ;  or  the  value  of 
the  three  right  hand  figures  maybe  found  by  inspection,  (as 
in  Case  V.  of  Decimals.) 

EXAMPLE. 

13.  In  $344  48  how  many  pounds,  shillings,  &c.  ? 

3 

£103,344         Or   by    344.48 
20         Inspec.         '  3 

s.  6,880  103.344 

12  6  10.i=value  of  ,344  by  in. 

d.  10,5GO 

4 


qrs.  2,240  Ans.  £103  6  1CU. 


FEDERAL  MONEY.  g£ 

CASE  X. 

To  reduce  dollars,  cents  and  mills,  to  pounds,  shillings,  pence 


js. 

RULE.  Multiply  the  given  sum  by  3  and  cut  off  four  right 
hand  figures,  and  proceed  as  in  Case  IX. 

EXAMPLE. 

14.  In  $116,46,6f  how  many  pounds,  &c.  ? 

3 

£34,9400 
20 

s.  18,8000 
12 

d.  9,6000 
4 

qrs.  2,4000  Ans.  £34  18  9J. 

CASE  XI. 

To  change  Sterling  to  Lawful  Money. 
RULE.  Add  i  to'the  Sterling  the  sum  will  be  Lawful. 

EXAMPLE. 

15.  In  £347  Sterling,  how  much  Lawful  ? 

3)347=sterling. 
115  13  4  added. 


£462  13  4=lawful.  Ans.  £462  13  4. 

CASE  XII. 

To  change  Lawful  to  Sterling  Money. 
RULE.  From  the  Lawful  subtract  £,  the  remainder  will 
be  Sterling. 

EXAMPLE. 

16.  Reduce  £462  13  4  Lawful  to  Sterling. 
4)462  13  4=lawful. 
115  13  4  subtract. 


£347  00  0=sterling,  Ans.  £347, 


g*j  FEDERAL  MONEY. 

CASE  XIII. 

To  reduce  New-England,  Virginia,  Kentucky  and  Tennessee 

currency  to  Federal  Money. 
RULE.  Add  a  cipher  to  the  pounds  and  divide  by  3. 

NOTE.  If  there  are  shillings,  pence,  &c.  given  in  any  case,  they 
must  always  be  reduced  to  the  decimal  of  a  pound  and  annexed  to 
the  given  pounds  before  dividing  by  3  ;  and  in  all  such  cases  three 
figures  must  be  cut  off  at  the  right  hand  for  decimals  of  a  dollar. 

EXAMPLES. 

17.  Reduce  £36  to  Federal  Money. 

3)360 

120  Ans.  $120. 

18.  Reduce  £45  16  to  Federal  Money. 

Ans.  8152,66,6f. 

CASE  XIV. 

To  reduce  New-York  and  North- Carolina  currency  to  Fed- 

eral  Money. 
RULE.  Add  a  cipher  and  divide  by  4. 

EXAMPLE. 

19.  Reduce  £44  New-York  and  North-Carolina  curren- 
cy to  Federal  Money. 

4)440 

110  Ans.  jgl  10. 

CASE  XV. 

To  reduce  New-Jersey.  Pennsylvania,  Delaware  and  Mary- 

land  currency  to  Federal  Money. 

RULE.  Multiply  by  8,  and  divide  the  product  by  3,  the 
quotient  will  be  the  answer. 

EXAMPLE. 

20.  Reduce  £243  New-Jersey  to  Federal  Money. 

8 

3)1944 

648=federal  money-  Ans.  $648. 


FEDERAL  MONEY.  93 

CASE  XVT. 

To  reduce  South-Carolina  and  Georgia  currency  to  Federal 

Money. 

RULE.  Multiply  by  30  and  divide  the  product  by  r,  the 
quotient  will  be  the  answer. 

EXAMPLE. 

21.  Reduce  £300  South-Carolina  and  Georgia  to  Feder- 
al Money. 

300 
30 

7)9000 

1 285,7  l,4f=federal.  Ans.  $1285,7J,4f . 

CASE  XVII. 

To  reduce  Canada  and  JVova  Scotia  currency  to  Federal 

Money. 
RULE.     Multiply  by  4,  and  the  product  will  be  dollars. 

EXAMPLE. 

22.  Reduce  £150  Canada  or  Nova  Scotia  to  Federal 
Money. 

150 
4 

(  600=Federal.  Ans.  $600. 

CASE  XVIII. 

To  reduce  Livres  Tournois*  to  Federal  Money. 
RULE.     Multiply  the  Livres  by  4  and  divide  by  21. 

EXAMPLE. 

23.  Reduce  1000  livres  to  federal  money. 

1000 
4 

21)4000(190,47,6/r.  Aug.  $190,47,6^. 

*  The  term  u  Tournois,"  when  applied  to  money  in  France, 
is  of  the  same  import  as  u  Sterling"  when  applied  to  money  in  Eng- 
land. 

9 


FEDERAL  MONEY. 


CASE  XIX. 

To  reduce  Federal  Money  to  New  England,  Virginia,  Ken- 
tucky and  Tennessee  currency. 

RTTI.F..  Multiply  by  3,  and  cut  off  three  right  hand  fig- 
ures, the  left  hand  figures  will  be  pounds,  the  figures  cut 
off,  decimals  of  a  pound,  the  value  of  which  may  be  found 
as  in  Case  IX. 

EXAMPLE. 

24.  Reduce  $345,69  to  Massachusetts,  &c.  currency. 

345,69 
3 

£103,707=£103  14  1|.         Ans.  £103  14  If. 

CASE  XX. 

To  reduce  Federal  Money  to  New   York  and  N.  Carolina 
currency. 

RULE.  Multiply  the  dollars  and  cents  by  4  and  cut  off 
three  right  hand  figures  for  decimals,  the  left  hand  figures 
will  be  pounds. 

EXAMPLE. 

25.  Reduce  $961,54|  to  New  York  and  N.  Carolina  cur- 
rency. 

961,541 
4 

£384,619=£384  12  41.  Ans.  £384   12  4£. 

CASE  XXI. 

To  reduce  Federal  Money  to  New  Jersey,  Pennsylvania, 

Delaware  and  Maryland  currency. 

RULE.  Multiply  by  3  and  divide  by  8,  cut  off  three 
right  hand  figures  for  decimals. 


FEDERAL  MONEY.  95 

EXAMPLE. 

26.  Reduce  $382  98  4  to  New  Jersey  currency. 

$382  98  4X3~8=£143  12  4i.          Ans.  143  12  4£. 

CASE  XXII. 

To  reduce,  Federal  Money  to  South  Carolina  and  Georgia 

currency. 

RULE.     Multiply  by  7  and  divide  by  30,  cut  off  three 
right  hand  figures  for  decimals. 

EXAMPLE. 

27.  Reduce  $530  01  to  South  Carolina  and  Georgia  cur- 
rency. 

530  01x7-*-30=£l23,669=Ans.  £123  13  4|. 

CASE  XXIII. 

To  reduce  Federal  Money  to  Canada  or  Nova  Scotia  cur- 
rency. 

RULE.     Divide  by  4,  the  quotient  will  be   pounds  and 
decimals. 

EXAMPLE. 

28.  Reduce  $494  50  8  to  Canada  or  Nova  Scotia  cur- 
rency. 

4)494.50,8 

£123,627     123  12  G-\.   Ans 

CASE  XXIV. 

% 

To  reduce  Federal  Money  to  Liures  Tournois. 
RULE.     Multiply  by  21  and  divide  by  4,  the   quotient 
will  be  livres. 

EXAMPLE. 

29.  Reduce  $190  47  6^f  to  Livres  Toiirnois. 

£190  47  6^X21-^4-^1000.  AIIS.  1000. 


96 


FEDERAL  MONEY. 


ADDITION  OF  FEDERAL  MONEY. 

RULE.     Place  the  several  denominations  under  each  oth- 
er, and  add  them  as  in  whole  numbers,  or  decimals. 

TABLE  OF  FEDERAL  MONEY. 

10  Mills  marked  m.  .     .        'make     1  Cent    marked     e. 

10  Cents 1  Dime     .     .     .     d. 

10  Dimes 1  Dollar    $  or  dolls. 


10  Dollars .1  Eug!e 


Eaj 


NOTE.  When  the  number  of  cents  is  less  than  10,  a  cipher  must 
always  be  written  in  the  place  of  dimes  ;  as  ,09=nine  cents,  &c. 

EXAMPLES. 

Add  8  eag.  6  dolls.  4  dim.  8  m. ; — 7  dolls.  6  dim.  7  cents, 
8  mills  ; — 8  dolls.  8  dim. — 9  dim.  8  cents  ; — 4  eag.  and  8 
mills  together. 


Eag. 

$ 

d. 

c. 

m. 

$• 

c. 

m. 

'  8 

6 

4 

0 

8 

. 

-       6 

40 

8 

7 

6 

7 

8 

1 

7 

67 

8 

8 

8 

0 

0 

$ 

8 

80 

0 

9 

8 

0 

It 

98 

0 

4 

0 

0 

0 

8 

c 

0 

40 

00 

8 

O 

14 

3 

y 

7 

4 

C/3 

i 

$143 

87 

4 

*  NOTE.     The  second  method  is  preferable,  and  is  adopted  in  this 
work. 

PKOOF.     As  in  whole  numbers. 

SUBTP^JICTION  OF  FEDERAL  MONEY. 

RULE.     Place  the  several  denominations  and    subtract 
them  as  in  whole  numbers,  or  decimals. 


EXAMPLES. 

1. 

2. 

3. 

$.     c.  m. 

$.    c.  m. 

C.     c.  m. 

From     873  28  2 

48 

348  43  3 

Take       87  34  7 

7  38  4 

97 

785  93  5  40  61  6 

i.  From  2  eagles  take  ,49  3  mills. 


251   43  3 
Ans.   1  9  50  7  rn. 


FEDERAL  MOXKY  0r 

MULTIPLICATION  OF  FEDERAL  MOXEY. 

CASE  I. 

To    multiply   the  several    denominations   by  any    given 

number. 

RULE.  Place  the  given  numbers  and  multiply  them  as 
in  whole  numbers,  or  decimals,  and  point  off  in  the  pro- 
duct as  in  the  multiplicand. 

• 

NOTE.  In  multiplying  no  regard  should  be  paid  to  the  decimal 
points. 

EXAMPLES. 

1.  2. 

$.   c.  m.  $.    c.   m. 

Multiply     4  83  6  Multiply     35  32  4 
by               8  by  11 

$38  68  8  $388  56  4 


3.  Multiply  §8  24  by  24 Ans.  $197  76. 

4.  .     .     •  $34  83  4  by  36 1254  02  4. 

5.  ....      74  8  by  49 36  65  2. 

6.  •     .     .     •      09  7  by  700 67  90. 

CASE  II. 

To  find  the  value  of  goods  in  Federal  Money. 
GENERAL  RULE. 

Multiply  the  price  by  the  quantity,  and  point  off  in  the 
product,  as  in  the  given  price. 

EXAMPLES. 

7.  What  will  8  yards  cloth  cost  a  g3  44  8  per  yd.  ? 

3  44  8=given  price. 
8=quantity* 

g<27  58  4=value  of  3  yds.         Ans.  g27  58  4. 


98 


FEDERAL  MONEY. 


Questions. 

8.  What  will  12  Ib.  cost  a  80,09,3  m.  per  Ib  ? 

yd.? 


9. 
10. 
11. 
12. 
13. 
14. 


24  yds. 

,83,8 

77  yds. 
149  Ib. 

,34 
7,30,3 

200  yds. 

,11,2 

1345  yds. 

.  ,23,3 

3480  Ib. 

.    ,29,1 

81  11  6. 

20  11  2. 
yd.?   26  18. 
"Ib.?  1088  14  7. 
yd.  ?   22  40. 
yd.?  313  38  5. 
Ib.  ?  1012  68. 


CASE  III. 


When  goods  are  bought  or  sold  by  the  cwt.  To  find  the  value. 
RULE.  Multiply  the  given  price  by  112,  or  by  7,  8  and 
2,  and  point  off  in  the  product,  as  in  the  given  price;  when 
/there  are  more  hundreds  than  one,  multiply  the  price  of 
one  hundred  by  the  given  number  of  hundreds. 

EXAMPLES. 

15.  What  will  1  cwt.  cost  a  S3  24  2  per  Ib.  ? 
3,24,2=given  price. 
112=lb.  in  cwt. 


38904 
3242 

363,K),4=value  cwt. 


Questions. 

16.  What  will  1  cwt.  cost  a 

81,08 

•     .     • 

17.         .     .       1  cwt.     • 

.    ,34,3 

. 

18. 

8  cwt.     .    . 

3,34 

•     . 

19. 

12  cwt.     .     . 

.    ,84,2 

.     . 

20. 

24  cwt.     .     . 

•    ,34 

.     .     . 

21. 

98  cwt.     .     • 

•    «OQ,7 

.     . 

22. 

180cw-t. 

,8 

mills 

Ans.  £363,10,4. 
^Answers. 
$120  96. 

38  41  6. 
2992  64. 
1131  64  8. 
913  92. 
954  91  2. 
161  28. 


CASE  IV. 

When  articles  are  bought  or  sold  by  the  thousand. 
RULE.     Multiply  the  price  by  the  whole  quantity  and 
cut  off  three  right  hand  figures  for  decimals,  the  left  hand 
figures  will  be  the  answer  in  the  lowest  denomination  men- 
tioned in  the  given  price. 


FEDERAL  MONEY.  gg 

NOTE.  When  the  quantity  is  a  greater  number  than  the  price, 
it  will  be  more  concise  to  multiply  the  quantity  by  the  price,  the  re- 
sult will  be  the  same. 

EXAMPLES. 

23.  What  will  24570  feet  of  boards  cost  a  g!8  75  perM.  ? 
18,75=given  price. 
24570=quantily. 

131250 
9375 
7500 
3750 


460,68,750=Ans.  Ans.  £460  68  7£. 

•U.  What  will  78455  bricks  cost  a  g3  25  per  AI.  ? 

Ans.  $(347  25  3|. 
'25.  What  will  43480  feet  joists  cost  a  g!5  30  per  M.  ? 

Ans.  g665  24  4, 

CASE  V. 

To  find  the  value  of  parts  of  any  quantity. 
RULE.  If  the  numerator  of  the  fractional  part  is  an 
unit,  divide  the  given  price  of  1  Ib.  1  yd.  &c.  by  the  denomi- 
nator of  the  fraction  ;  but  if  the  numerator  is  more  than  1, 
multiply  the  price  by  the  numerator,  and  divide  the  pro- 
duct by  the  denominator,  the  quotient  will  be  the  answer. 

EXAMPLES. 

26.  What  will  |  of  a  yard  cost  a  $4  84  per  yard  ? 
denominator    8)4,84=price  1  yd. 

,60,5=value  of  \  yd.       Ans.  gO  60  5. 

27.  What  will  £  of  a  yard  cost  a  £4,84  per  yard  ? 

4,84=price  1  yd. 
3=numerator. 


denominator  8)14,52 


gl,8155=value  off  yd.  Ans.  81,81,5. 

28.  What  will  ||  of  a  dozen  cost  a  g9,50  per  dozen  ? 

Ans.  g8,70,8i. 

29.  What  will  TV  of  a  Ib.  cost  a  $8,12  per  Ib.  ? 

Ans.  gO,81,2. 


FEDERAL  MONEY. 


CASE  VI. 

When  the  quantity  is  a  mixt  numler. 
RULE.     Multiply  the  price  by  the  whole  number,  and 
for  the  fractional  part,  work  as  before  5  or  reduce  the  mixt 
number  to  an  improper  fraction  and  proceed  as  in  Case  V. 

EXAMPLES. 

30.  What  will  18£  yards  cost  a  $3,84  per  yard  ? 

3,84=price  1  yd.         3,84  Or,  ISf^f1. 

18=whole  number.        7=numer.    3,84x151—8  = 

$72,48  as  before. 

3072  denom.  8)26,88 

384  

$3,36=value  |  yd. 

69,12=value  18  yds. 

added  3,36= value  £  yds. 

$72,48= value  18|  yds.  Ans.  $72,48. 

Questions.  Answers. 

31.  What  will  24£  yards  cost  a  $3,24  per  yd.  ?  $79,38. 

,84,6  36,16,6$. 

4,38 
3,08 

,13,3 


32. 
33. 
34. 
35. 
36. 
37. 
38. 

.   42|  yds. 
69f  yds. 
.   139|  yds. 
•   294|  yds. 
•   500±  yds. 
•   348|  doz. 
.  lOOOfyds. 

4,00,8 


304,95,7^. 
430,76. 
39,1 9,0|. 
2005,00,2. 


,8m.pr.dz.  2,79. 
,34,8      .  348,21,7$, 


DIVISION  OF  FEDERAL  MONEY. 

CASE  I. 
GENERAL  RULE. 

Place  the  numbers  and  divide  them  as  in  whole  numbers, 
or  decimals,  and  the  quotient  will  be  the  answer  in  the 
same  denomination  as  the  lowest  in  the  dividend,  which 
may  be  reduced  to  its  proper  denomination. 

PROOF.     By  Multiplication. 

NOTE.  When  the  quantity  is  a  composite  number,  divide  the 
price  by  the  component  parts,  which  make  the  quantity. 


FEDERAL  MONEY. 


£01 


EXAMPLES. 


1.  Divide  $34,48,4  by  4. 
4)34,48,4 


2.  Divide  $434,88  by  12. 
12)434,88 


$8,62,1  Ans. 

Dividends.  Divisors 
.  Divide  $197,76  by  24 


36,65,2 

10,50 

67,90 


by  49 
by  125 
b  700 


$36,24  Ans. 


Quotients. 
$8,24 
,74,8. 
,08,4. 
,09,7. 


CASE  II. 

To  find  the  value  of  1  yd.  1  Ib.  $c.  in  Federal  Money. 

RULE.  Divide  the  whole  value  by  the  whole  quantity, 
and  the  quotient  will  be  the  answer  in  the  lowest  deuouii- 
nation  to  which  the  dividend  was  reduced. 


EXAMPLES. 

7.  If  8  yards  cost  $27,58,4  what  will  1  yd.  cost  ? 
whole  quantity  8)27,58,4=value  of  the  whole  quantity. 


$3,44,8=priee  of  1  yd. 


Ans.  $3,44,8. 

Answers. 


Questions. 

8.  If  12  Ib.  cost    §1,11,6  what  will  1  Ib.  cost  ?  $0,09,3 

9.  24yds. 

10.  77  yds. 

11.  149  "ib. 

12.  1345  yds. 

13.  200yds. 

14.  3480  Ib. 


rn 


20,11,2 
26,18 

,83,8. 
,34. 

1088,14,7 
313,38,5 
22,40 
1012,08 

.      7,30,3. 
,23,3. 
.         .         .        ,11,2. 
.        ,29,1. 

CASE  III. 

When  goods  are  bought  or  sold  by  the  cwt,     To  find  the 

value  of  1  Ib. 

RULE.  Divide  the  given  value  by  112,  or  by  7,  8  and  2, 
the  last  quotient  will  be  the  answer,  in  the  same  denomU 
nation,  to  which  the  dividend  was  reduced. 


103 


FEDERAL  MONEY. 


EXAMPLES. 
15.  If  1  cwt.  cost  $363,10,4  what  will  1  lb.  ? 


112)363,10,4(3,24,2. 
336 


271  Or  thus- 


7)363,10,4 
8)51,87,2 
2)6,48,4 
$3,24,2  as  before. 


470 
448 

224 
224 

0 

Questions. 
16.  If  1  cwt.  cost  $120,96  what  will  1  lb.  cost? 


17.    1 

38,41,6 

18.    8 

2992,64 

19.   12 

1131,64,8 

20.   24 

913,92 

21.   98 

954,91,2 

22.  180 

161,28 

Aus.  $3,24.2. 
Jlnswers, 
$1,08. 

,34,3.* 
3,34. 
,84,2. 
,34. 
,08,7. 
,00,8. 


CASE  IV. 


When  articles  are  bought  or  sold  by  several  thousands,  to 

find  the  price  of  one  thousand. 

RULE.  To  the  given  price  annex  three  ciphers,  and  di- 
vide it  by  the  given  quantity,  the  quotient  will  be  the  price 
of  one  thousand,  in  the  lowest  denomination  in  the  given 
price. 

EXAMPLES. 

23.  If  24570  feet  of  boards  cost  8460,68,7$,  what  will  1  M. 
cost?  A  ns.  $18,75. 

21.  If  78455  bricks  cost  $647,25,33,  what  will  1  M.  cost  ? 

Ans.  $8.25 

25.  If  43480  feet  joists  cost  $665,24,4,  what  will  1  M.cost? 

Ans.  $15,30. 

CASE  V. 

When  the  quantity  is  a  fraction  to  find  the  value  of  one. 
RULE.     If  the  numerator  is  an   unit,  multiply  the  given 
value  of  1  lb.  &c.  by  the  denominator  of  the  fraction  ;  but 


FEDERAL  MONEY. 

if  the  numerator  is  more  than  1,  multiply  the  given  value 
by  the  denominator  and  divide  the  product  by  the  numera- 
tor, the  quotient  will  be  the  answer. 
EXAMPLES. 

26.  If  }  of  a  yard  cost  $0,60,5,  what  will  1  yard  cost  ? 

,60,5=given  value. 
8=denomiuator. 

$4,84,0=  value  of  1  yard.  Ans.  $4,84. 

27.  If  |  of  a  yard  cost  $6,43,2,  what  will  1  yard  cost  ? 

6,43,2=given  value. 
4=denominator. 

numerator  3)25,72,8 

$8^57,6=  value  of  1  yd.  Ans.  $8,57,6. 

•-23.  If  |i  of  a  dozen  cost  $8,70,8*-,  what  will  1  dozen  cost? 

Ans.  $9,50. 

29.  If  TV  of  a  Ib.  cost  $0,81,2,  what  is  it  a  lb.?  Ans.  $8,12. 

CASE  VI. 
When  the  quantity  is  a  inioct  number,  to  find  the  value  of 

1  lb.  1  yd.  #c. 

RULE.  Multiply  the  whole  number  by  the  denominator 
of  the  fraction,  adding  to  the  product  the  numerator;  place 
it  over  the  denominator,  then  multiply  the  given  value  by 
the  denominator,  and  divide  the  product  by  the  numerator. 
the  quotient  will  be  the  value  of  1  lb.  &c. 
EXAMPLES. 

30.  If  18£  yards  cost  $72,48  what  will  1  yard  cost  ? 
18  =  whole  number.  Then  72,48=given  value. 

8=denominator.      And,  1f1  8=denominator. 


144  numerator  151)579,84(3,84=value  1  yd. 

7=numerator  added. 

151—  new  numerator.  Ans.  $3,84. 

Q'iostions.  Jln&werz. 

31.  Ii'24£  yds.  cost  §79,38  what  will  1  yard  ?      83,24. 

32.  421yds.     .        36.16.6$  .        ".         .  ,84,6. 

33.  69f  yds.     .     304,95,7^  .         .         .         4,38. 

34.  139f  'yds.  .     430,76  .         .         .  3,08. 

35.  294|yds.  .       39.19,0f          .         .         .  ,13,3. 

36.  500|  'yds.  .   2005,00,2  ...         .  4,00,8. 

37.  348$  doz.  .         2,79       ....                ,8. 


PRACTICE. 


PRACTICE. 

PRACTICE  is  a  contraction  of  the  Rule  of  Three,  when 
the  first  term  happens  to  be  an  unit,  and  is  a  concise 
method  of  finding  the  value  of  goods. 

Perhaps  no  method  can  be  more  simple  and  concise  to  find  the 
value  of  goods  in  Federal  Money,  than  the  general  rule  of  multiply- 
ing the  price  by  the  quantity,  as  given  in  Multiplication  of  Federal 
Money  ;  therefore,  the  application  of  this  rule  to  Federal  Money  is 
almost  useless.  Yet  as  English  merchants,  trading  with  Americans, 
make  out  the  invoices  of  their  goods  in  sterling  money,  an  acquain- 
tance with  this  excellent  rule  is  necessar}-  to  every  one,  employed  in 
mercantile  pursuits. 

Questions  in  this  rule  are  performed  by  taking  the  aliquot,  or 
even  parts.  The  following  table,  therefore,  should  be  committed  to 
memory,  or,  at  least,  the  rule  for  making  it  well  understood,  by  the 
scholar. 

TABLE  OF  ALIQUOT,  OR  EVEN  PARTS. 


Aliquot  parts  of  a  shifting,  j    Jlliquot  parts  of  a  penny.     \ 
d.  qrs. 

is  equal  to  TV  of  a  shilling.  £  is  equal  to     f  of  a  penny. 


Jlliquot  parts  of  a  ton. 

CU't. 

_10*is    equal    to  ±  of  a  ton. 

~    5=       -     -     -     I     -     -     - 


Jlliquot  parts  of  a  pound.  \  4=. 


s. 


1  is  equal  to  JT  of  a  pound.    *(> 


21= 

* 


1.4= 


To      ' 


1,8-      -     -  ^  -  -  -  -  j      jMquot  parts  of  a  cwt. 

~  To"  '  '  -  '   'qrs.     Ib. 

2,6=     -     -  J.  -  -  .  .   2  or  56==     .     .     i  of  a  cwt. 

3.4=     -     -  i  -  -  -  -  |i  or  28=     -     -           -     -     - 


4  = 

5  = 
6.8= 
10  = 


14=     -     -     |     -     -     - 
i 

T 


16=     -      -     * 


7=     -     -    A 
4=     -     -    •£> 


PRACTICE.  406 

Rules  to  find  the  aliquot  parts  which  any  given  pence, 
shillings,  pounds,  &c.  make  of  a  s.  £.  ton,  cwt.  or  £  cwt. 

To  find  the  aliquot  part  of  a  shilling. 
RULE.     Divide  I2d.  by  the  given  number  of  pence,  the 
quotient  will  be  the  aliquot  part  of  a  shilling. 

EXAMPLE. 
What  part  of  a  shilling  is  4d.  ? 


-Mt=i  Ans. 


To  find  the  aliquot  part  of  a  pound. 

RULE.  Divide  20s.  by  the  given  number  of  shillings, 
the  quotient  will  be  the  aliquot  part  of  a  pound. 

EXAMPLE. 

What  part  of  a  pound  is  5s.  ? 

20-7-5=^  Ans. 

To  find  the  aliquot  part  of  a  ton. 

RULE.  Divide  20  cwt.  by  the  given  hundreds,  the  quo- 
tient will  be  the  aliquot  part  of  a  ton. 

EXAMPLE. 
What  part  of  a  ton  is  5  cwt. 

20-7-5=i  Ans. 

To  find  the  aliquot  part  of  a  cwt. 

RULE.  Divide  112  Ib.  by  the  given  number  of  Ibs.  thfc 
quotient  will  be  the  aliquot  part  of  a  cwt. 

EXAMPLE. 

What  part  of  a  cwt.  is  16  Ib.  ? 
112—16=^  Ans. 

To  find  the  aliquot  part  of  %  cwt. 

RULE*  Divide  56  Ib.  by  the  given  pounds,  the  quotient 
will  be  the  aliquot,  or  even  part. 

EXAMPLES. 

What  even  parts  of  \  cwt.  are  14  Ib.  8  Ib.  and  7  Ib.  ? 
56-r-14=i  Ans.         56-r-8=4  Ans.          56-r-7=j  Ans. 

NOTE.  By  these  rules  the  preceding  tables  may  be  easily  made, 
or  the  aliquot  part  of  any  given  price  be  found  ;  that  is,  by  dividing 
the  integer  by  any  given  number  of  the  same  name,  which  will  divide 
rt  without  a  remainder,  the  quotient  will  be  the  even  or  aliquot  part, 

10 


106 


PRACTICE. 


To  find  the  value  of  goods. 
GENERAL  RULE. 

1.  Suppose  the  price  of  the  given  quantity  to  be  Id.  Is.  I  £,.  per 
yd.  &c. ;  then  the  given  quantity  itself  would  be  the  answer  at  the 
supposed  price. 

2.  Divide  the  given  price  into  aliquot  parts,  either  of  the  suppose'! 
price,  or  of  one  another,  and  the  sum  of  the  quotients  belonging  to 
each  will  be  the  true  answer  required. 

CASE  I. 

When  the  price  is  farthings. 

RULE.  Find  the  value  of  the  given  quantity  at  a  penny 
per  Ib.  or  yd.  &c.  then  divide  by  the  aliquot  parts  of  a  pen- 
ny;  and  by  12  and  20,  the  last  quotient  will  be  the  answer. 

EXAMPLES. 
1.  What  will  4678  yds.  cost  at  I,  -h  and  |  per  yard  ? 


d. 


4678  a  i  per  yard. 


12      1169J 
2,0          9,7 

£4  17  5i  Ans. 
4678  yards  a  §  per  yard. 

4678  yards  a  f  *  per  yard  ? 


Ans.  £9  14  11. 
Ans.  £14  12  4£. 


*  In  all  cases  where  the  given  price  is  not  an  even  part  it 
must  be  reduced  into  even  parts,  and  the  sum  of  the  quotients  will  be 
the  answer. 

CASE  II. 

When  the  price  is  pence. 

RULE.     Find  the  value  of  the  given  quantity  at  Is.  per 
.  Ib.  &c.  ;  then  divide  by  the  aliquot  part,  or  parts,  and 


yd.  Ib. 
fey  20  : 


the  last  quotient  will  be  the  answer. 


PRACTICE. 


107 


2. 
d. 
.6 


EXAMPLES. 

d.   d.  d.  d.  J.  d. 

What  is  t'?e  value  of  8745  yards  cloth  a  1-1-0-2-^-4-5 
d.  d.  d.  d.  d. 

-7-8-9-10  and  1.1,  per  yd. 


d.       s. 

w. 

<¥  . 

1 

i 
TV 

8745  yds. 

4 

1 

3 

8745  yds.  a  bd. 

— 

2915 

2,0 

72,8  9 

1 

\ 

723  9 

£36  8  9  Ans. 

2.0 

364  ,3  9 

n 

1 

8745  yds. 

£182  3  9  Ans. 

2,0 

109,3  H 

Questions.         Answers. 
3.  8745  \d«  a  6d. 

£54  13   1|   Ans. 

£218   12  6. 
4.     .     .     .aid. 

2 

* 

87  15  yds. 

£255  1   3. 



5.     .     .     -    a  8e?. 

2,0 

145  ,7  6 

£291   10. 

-  — 

6.     .     .     .    a  9d. 

£72  17  6  Ans.  . 

£3^7  18  9. 

3 

JL 

8745  yds. 

7.     ...    a  Wd. 

_ 

£364  7  6. 

2,0 

218,6   3 

8.     .     .     .    a  lid. 

,  

£400  16  3. 

£109  6   3 

9.  87433  a  9d. 

4 

l 

3 

8745  yds. 

£327   17  7|. 
10-  840}  a  lOd. 

2,0 

291   ,5 

£35  0  7*. 

—  .         

11.  3800  Ib.  a  Hi. 

£145  15  Ans. 

1                    S182   1   8. 

CASE  III. 

When  the  price  is  shillings  and  pence. 

RULE.  Find  the  value  of  the  given  quantity  a  l£  per 
yd.  Ib.  &e.  then  divide  by  the  aliquot  part  or  parts,  the 
quotient  will  be  the  answer  in  pounds. 


108  PRACTICE. 

EXAMPLES. 

S.    S.    S.    S.  S. 

12.  What  will  8845  yards  cosl  a  1-2-3-4  and  5  per  yd.  H 


£. 
fa 

8845  yds. 
£442  5  Ans. 

Questions. 

13.  What 
14.     ,     . 
15.     .     . 
16.     .     . 
17.     . 
18.     .     . 
19.     .     . 
20.     »    . 
21.     .     . 

Answer*. 
cost  5674  Ib.  at  3  4d. 
perlb.  ?     £945  13  4 
.     7484£  Ib  a  6  80?. 
£2494  16  8. 
.     8450£  Ib.  a  9  8rf. 
£4084  5  9. 
.     7484|  vds.  alold. 
£4939   16  8. 
•     8796  ^b    .  a  17  4d. 
£7623  12  8. 
.     3000  Ib.  a  2  6rf. 
£375. 
.     734§  a  16s. 
£587  12. 
,    8040|  a  16  8rf. 
£6700  12  6. 
.    1250£  a  18*. 
£1125  4  6. 

To" 

8845  yds. 
£884  10  Ans. 

TU 
i 

8845  yds. 

884  10 
442     5 

£1326   15  Ans. 

J 

8845  yds. 
£1769  Ans. 

J 

8845  yds. 
£2211  5  Ans. 

CASE  IV. 

the  price  is  pounds,  shillings,  pence  and  farthings. 
RULE.     Multiply  the  given  quantity  by  the  pounds  ;  for 
the  rest  take  parts. 

EXAMPLES. 

22.  What  will  8464  yards  cost  a  £3  6  8  per  yard  ? 

t.d. 
"  |  6  8  ||  I  8464=quantity. 

3=given  pounds. 

25392 
2821  6  8 


£28213  6  8  Ans.  £20213  6  8. 

23.  What  will  7848  Ib.  cost  a  £2  7  1H  per  Ib.  ? 

Ans.  £10818   17. 


TARE  AND  TRET. 


109 


24.  What  will  2157  yards  cost  a  £3  15  2$  per  yard  ? 

Ans.  £8108  19  5£, 

25.  What  will  4374£  Ib.  cost  a  £7  10  H  per  Ib.  ? 

Ans.  £32836  1  9*. 

CASE  V. 

When  the  price  and  quantity  are  both  of  several  denomina 

tions. 

RULE.     Multiply  the  price  by  the  integers  of  the  quan- 
tity and  take  parts  of  the  integer  for  the  rest. 

EXAMPLES. 

26.  What  is  the  value  of  7  2  14  Ib.  a  £3  10  14|  per  cwt.  ? 

qrs.  cwt. 

3  10  4i=given  price. 
7=integers. 


14lb 


£26  16  7*  Ans.  £26  16  7*. 

27.  What  will  4  3  24  Ib.  cost  a  $4,48  per  cwt. 

Ans.  $22,24. 

28.  What  will  12  1   18  Ib.  cost  a  $8,36,8  per  cwt. 

Ans.  $103,85,2. 


TARE  AND  TRET. 

TARE  AND  TRET  are  rules  for  deducting  certain  al- 
lowances, made  by  the  seller  to  the  purchaser,  for  the 
weight  of  the  thing  which  contains  the  goods. 

These  allowances  are  made  either  at  so  much  for  the 
box,  bag  or  barrel,  at  so  much  per  cent,  or  so  much  in  the 
gross  weight. 

1.  Tare  is  an  allowance  for  the  weight  of  the  box,  bag, 
or  barrel,  containing  the  goods. 

2.  Tret  is  an  allowance  of  4  Ib.  on  every  104  Ib.  for 
waste. 

10* 


110  TARE  AND  TRET, 

3.  Cloff is  an  allowance  of  2  Ib.  on  every  3  cwt.  made  t<* 
the  people  of  London  only. 

4.  Gross  weight  is  the  whole  weight  of  the  goods,  togeth- 
er with  the  thing  containing  them. 

5.  Suttle  weight  is  when  part  of  the  allowances  is   de- 
ducted from  the  gross. 

6.  Net  weight  iS  the  pure  weight  of  the  goods,  when  all 
allowances  are  deducted. 

CASE  I. 

When  tare  is  so  much  per  box,  bag,  or  barrel,  <$*c. 
RULE.     Multiply  the  number  of  boxes,  bags  or   barrels, 
&c.  by  the  tare,  and  subtract  the  product  from  the  gross, 
the  remainder  will  be  the  net  weight. 

EXAMPLES. 

1.  What  is  the  net  weight  of  24  hhds.  of  tobacco,  weigh- 
ing 143  2  1.4  Ib.  gross  ;  tare  84  Ib.  per  hhd.  and  what  is 
the  value  at  $7,25  per  cwt.  ? 

84ajfarc.  143  2  14=gross. 

24==nuniber  hhds.  18  0    0=tare. 


336  125  2  14  lb.=net. 

168 

!12)2016(18=tare. 
112 

896 
896 

A       025  2  14  lb. 

0  Ans'  J  $910,78,1*. 

2.  In  241  barrels  of  figs  each  weighing  3  19  lb.  gross; 
tare  10  lb.  per  barrel;  how  many  pounds  net,  and  what  is 
their  value  at  15f  cents  per  lb.  A  C 22413  lb. 

A       I  $3530,04,7$. 

CASE  II. 

When  tare  is  so  much  in  the  whole  gross  weight. 
RULE.     Subtract  ibe  given  tare  from  the  gross,  the  re- 
mainder will  be  the  net. 


TARE  AND  TRET. 

EXAMPLES. 

3.  Having  deducted  the  tare,  what  is  the  value  at  $6,50 
per  c\vt.  of  83   hhds.  tobacco,  weighing  137  cwt.  gross  ; 
tare  678  Ib.  in  the  whole  ?  Afl        >  £851,15,l|i. 

|  130  3  22  Ib. 

4.  At  10£  cents  per  Ib.  what  is  the  value  of  184  boxes 
of  raisins,  each  weighing  33  Ib.  gross  5  tare  152  Ib.  in  the 
whole  ?  A        S  $606,80. 

CASE  III. 

Wlien  the  tare  is  so  much  per  cwt. 

RULE.  Divide  the  gross  by  the  aliquot  part,  which  the 
tare  makes  of  a  cwt.  as  in  Practice  ;  subtract  the  quotient 
from  the  gross,  the  remainder  will  be  the  net. 

EXAMPLE. 

5.  What  is  the  net  weight  of  24  boxes  of   sugar,  each 
weighing  7213  Ib.  gross  ;  tare  14  Ib.  per  cwt.  and  what 
is  the  value  at  $11,75  per  cwt.  ? 

7  2  13  lb.=l  box. 


30  1  24=weight  of  4  boxes. 
6 

).    cwt.  

14U  1182  3     4=weight  of  24  boxes. 
I     I  22  3  ll=lare. 

159  3  21  lb.=net  (159  3  21  Ib, 

?g!879,26,5f. 

6.  At  $10,50  per  owt  what  is  the  value  of  12  hhds.  su- 
gar, the  gross  weight  being  93  1   19  Ib.  ;  tare  18  Ib.  per 
cwt.?  A       <  $823,26,5f . 

s-}78  1   17 J  Ib. 

7.  What  is  the  net  weight  of  443  cwt.   tallow  gross  ; 
tare  17  Ib.  per  cwt.  and  what  is  the  value  a  10£  cents  per 
Ib.  ?  A        C375  3  1  Ib. 

3'  1 84418,92,5, 

CASE  IV. 

When  tret  is  allowed  with  tare. 

RULE.     Deduct  the  tare  as  before  directed,  tlen  divide 
the  suttle  weight  by  26,  (which  is  the  aliquot  part  that  4 


TARE  AND  TRET. 


Ib.  make  on  every  104  Ib.)  am!  the  quotient  will  be  the 
tret,  which  subtracted  from  the  stittle,  the  remainder  will 
be  the  net. 

EXAMPLES. 

8.  What  is  the  net  weight  of  a  hhd.  tobacco,  weighing 
14  3  27  Ib.  gross  ;  tare  16  Ib.  per  cwt. ;  tret  4  Ib.  per  104 
Ib. ;  how  many  pounds  net,  and  what  is  the  value  at  6| 
cents  per  Jb.  ? 

14  3  27=gross. 
4 

59 
28 


Ib.     cwt. 
16 


C  1383  14  oz. 


479 
120 

1679=gross  Ib. 
239  13oz. 

1439  3=suttle. 
|      |       55  5=tret. 

Ib.  1383  14oz.=net. 


9.  What  is  the  net  weight  of  4  hhds.  sugar,  weighing  as 
follows;  viz. 

No.  1.         8314  Ib. 

2.  4  2  19 

3.  7  1   14 

4.  14  2  23  gross  ;  tare  19  Ib.  per  cwt.  and  tret  as 
usual,  and  what  will  it  come  to  a  $12,25  per  cwt.  ? 

A       528   1  21  Ib. 
s>  I  $348,35,9  f 

CASE  V. 

When  doff  is  allowed  with  tare  and  tret. 
RULE.  Deduct  the  tare  and  tret  as  before  directed,  then 
divide  the  guttle  by  168  (it  being  the  aliquot  part  which  2 
Ib.  make  on  every  3  cwt.)  the  quotient  will  be  the  cloff, 
which  subtracted  from  the  suttle,  the  remainder  will  be  the 
net. 


DUODECIMALS. 


113 


EXAMPLE. 

10.  \Yhat  is  the  net  weight  of  15  3  20  Ib.  gross;  tare 
7  Ib.  per  c\vt.  ;  tret  and  cloft'as  usual. 
Ib.     cwt. 

15  3  20=gross. 
3  27  8=tare. 


14  3  20  8=suttle  tare. 
2     8  5=tret. 


14  1   12  3=suttle  tret. 
9  9=cloff. 


14  1     2  10=net. 


Ans.  14  1  2 


DUODECIMALS, 

OR  CROSS  MULTIPLICATION. 


DIMENSIONS  are  taken  in  feet,  inches,  and  parts  called 
seconds. 

Glaziers'  and  Masons'  work  is  measured  by  the  foot. 

Painting,  plastering,  paving  are  done  by  the  yard. 

Partitioning,  flooring,  slating,  rough-boardfng,  by  the 
square  of  100  feet. 

Stone  and  brick  work  by  the  rod  of  16£  feet,  whose 
square  is  272:}.  Bricks  also  are  laid  by  the  thousand. 

« 

GENERAL  RULE. 

1.  Under  the  multiplicand  write   the  corresponding  de- 
nominations of  the  multiplier. 

2.  Multiply  each  term  in  the  multiplicand,  beginning  at 
the  lowest,  by  the  feet  in  the  multiplier,  setting  each   re- 
sult under  its  respective  term,  observing  also  to  carry  for 
every  12  from  each  lower  to  the  next  higher  denomination. 

3.  Pro  *eed  in  the  same  manner,  and  multiply  the  multi- 
plicand by  the  inches  in  the   multiplier,  setting  the  result 
of  each  term  one  place  more  to  the  right  hand  of  those  in 
the  multiplicand 


DUODECIMALS. 


4.  In  the  same  manner  multiply  by  the  seconds  (parts) 
in  the  multiplier,  setting  the  result  of  each  term  one  place 
more  to  the  right  of  the  last,  and  so  on  for  thirds,  fourths, 
&c. 

NOTE.     Shillings  and  pence  may  be  multiplied  as  feet  and  inches. 


EXAMPLE. 

1. 

2. 

3. 

4. 

feet.  in. 

feet.  in. 

s.  d. 

s.  d. 

Multiply   3     4 

6  3 

2  3 

1  6 

by   7  10 

8  6 

2  3 

1   6 

23     4 

50  0 

4  6 

1   6 

294 

3  1  6 

6  9 

9  0 

feet.  26     1   4  feet.  53  1  6         s.  5  0  9         s.  2  3 
APPLICATION  OF  DUODECIMALS. 

1.  Measuring  by  the  foot  square,  as  glaziers-  and  masons' 

work. 

5.  There  is  a  house  with  4  tiers  of  windows,  and  4  in 
each  tier,  the  height  of  the  first  is  7  2  in.  (lut  second  6  8 
in.  the  third  5  9  in.  the  fourth  4  6  in  the  breadth  of  each 
3  10  in.  ho-v  nany  feet  square  are  in  the  windows,  and 
how  much  will  the  glazing  come  to  a  20  cents  per  foot  ? 
Fi^tlier  y  2  in.  "  feet  24  l=height. 

Second       6  8  4=numb.  windows. 

Third         5  9  

Fourth       46  96     4 

3  10=breadth. 

feet  24  1= whole  height.        

289 
80  3  4 


feet  369  3  4=whole  contents, 
20  cents  per  foot  is  $73,86,6f  . 


Ans  e*>  4 

"^73,86,61^ 

II.  Measuring  by  the  yard  square,  as  paviers',  painters', 
plasterers'1  and  joiners'*  work. 

NOTE.     Divide  the  square  feet  by  9,  the  quotient  will  be  square 
yards. 


DUODECIMALS 


EXAMPLE. 

6.  A  room  is  to  be  ceiled,  whose  length  is  74  9  in.  and 
width  11  6  in.  what  number  of  yards  square  is  in  the  room, 
and  what  will  the  work  amount  to  at  25  cents  per  yard  ? 

Ans 


III.  Measuring  by  the  square  of  100  feet,  as  rough  board- 

ing, slating*  shingling,  flooring,  and  partitioning. 
RULE.     Multiply  as  before,  and  cutontwo  right  hand 
figures  in  the  integers.  / 

EXAMPLES. 

7.  In  175  10  in.  long  and  9  10  in.   high  of  partitioning 
how  many  squares  ?  Ans.  17  squ.  29  f.  4  pts. 

•~  8.  What  will  the  slating  of  a  house  cost  at  $2,25  per 
square  of  100  feet  ;  the  roof  being  48  feet  in  length  and 
14  10  in.  wide,  and  how  many  squares  <l«es  it  contain  ? 

.        J  £32,04. 

-  £  14  squares,  24  feet. 

IV.  Measuring  by  the  rod. 

NOTE.  Bricklayers  value  their  work  at  the  rate  of  a  brick  and  a 
half  thick  ;  and  if  the  thickness  of  the  wall  is  more  or  less,  it  must  be 
reduced  to  that  thickness,  which  may  be  done  by  the  following, 

RULE.  Multiply  the  area  of  the  wall  by  the  number  of  the  half 
bricks  in  the  thickness  of  the  Avail,  the  product  divided  by  3  will  give 
the  area. 

EXAMPLE. 

*—  9.  If  a  brick  wall  is  4G35  feet,  and  thickness  2§  bricks  -, 
how  many  rods  does  it  contain  ?  Ans.  25  rods. 

V.  To  measure  a  ship's  tonnage  by  carpenters7  measure. 
RULE.  Multiply  the  length,  (of  single  decked  vessels^ 
breadth  at  the  mwin  beam,  and  depth  of  the  hold,  continu- 
ally together,  and  divide  the  product  by  95,  the  quotient 
will  be  the  tons  of  such  vessel. 

EXAMPLE. 

10.  What  1s  the  tonnage  of  a  single  decked  vessel,  whose 
keel  is  75  fret  long,  breadth  at  the  beam  22  feet,  and  the 
i    hold  10  6  in.  ? 

I  75X22X10|  =  17325-7-95=182/9  tons. 

Aus.  182TV  tons 


DUODECIMALS. 


VI.    To  find  the  tonnage  as  established  by  the  laws  of  the 
United  States. 

RULE.  1.  If  the  vessel  is  double  decked,  the  length 
taken  from  the  forepart  of  the  main  step  to  the  after  part 
of  the  stern  post  above  the  upper  deek  ;  the  breadth  at  the 
broadest  part  above  the  main  wales,  half  of  which  breadth 
is  the  depth  of  such  vessel  ;  deduct  from  the  length  three- 
fifths  of  the  breadth,  and  multiply  the  remainder  by  the 
breadth,  and  that  product  by  the  depth,  and  divide  by  95, 
the  quotient  will  be  the  tons  of  such  vessel. 

2.  If  the  vessel  is  single  decked,  take  the  length  and 
breadth  as  before  directed,  then  deduct  from  said  length 
three  fifths  of  the  breadth  and  take  the  depth  from  the  un- 
derside of  the  deck  plar.k  to  the  ceiling  in  the  hold, 
multiply  aud  divide  as  before,  the  quotient  will  be  the  tons 
of  such  vessel. 


EXAMPLES. 

11.  What  is  the  tonnage  of  a  single  decked  vessel  of  the 
following  dimensions,  viz.  the  length  80  6  in.  the  breadth 
at  the  main  beam  22  6  in.  and  the  depth  of  the  hold  9  6  in. 
government  tonnage  ? 

80  6=length. 
13  6=|  breadth. 


1507  6 

9  6— depth, 

13567  6 
753  9  0 


95)14321  3  (150JJ  tons,        Ant.  150JJ  tons,  3  part*. 


DUODECIMALS, 

12.  What  is  the  tonnage  of  a  double  decked  vessel, 
whose  length  is  70  6  in.  breadth  22  6  in.  and  depth  10  9  in. 
government  tonnase  ? 

70  6=length.  95)13786  10  6)145*}  tons, 

13  6=|  breadth.  95 

57  0  428 

22  6=breadth,  380 

1254  0  486 

28  6  475 


1282  6  11 

10  9=depth, 

12825  0 
961    10  6 


13786  10  6  Ans.  145*4  tons, 

VII.  To  measure  a  round  cistern. 

RULE.  Multiply  the  diameter  of  the  top  and  bottom  to- 
gether ;  from  the  product  subtract  *  of  the  square  of  their 
difference  ;  multiply  the  remainder  by  the  length  of  the 
stave  or  cistern,  the  product  will  be  the  solid  contents  in 
such  parts,  as  those  in  which  the  dimensions  are  taken  ; 
If  the  dimensions  are  taken  in  inches,  divide  by  359  for 
beer  or  water  and  294  for  wine  gallons. 

NOTE.     100  gallons  of  water  are  equal  to  a  hogshead. 

EXAMPLE. 

13.  How  many  hogsheads  of  water,  each  containing  100 
gallons,  will  a  cistern  contain,  measuring  at  the  top  diam- 
eter 4  feet,  the  bottom  4  6  in.  and  the  length  10  feet  ? 

4  =  48  in.  top  diam.    2580 

4  6=54  bottom diam.        123 

192  359)309600(859-4-100=3  hhds.  59  gals, 

240 

2592 
deduct  12=i  square  difference. 

2580  \ns.  8  hhcls.  59  gals. 

11 


DUODECIMALS. 

13.  How  many  hogsheads  of  water  and  how  many  gal- 
Ions  of  wine,  will  a  cistern  contain,  whose  dimensions   are 
as  follows  ;  viz.  the  diameter  at  the  top  3  feet,  the  bottom 
3  6  in.  and  the  length  of  the  cistern  8  feet? 
3     =     36=top  diameter.   1500 
3  6  in.=42=bottom  diam.        96=inches  in  length. 

72  9000 

744  13500 


1512  359)144000(401=4  hhds.  1    gal.  water 

deduct  12=isqu.ofdif.l436  or  beer. 

1500  400 

359 

41  ,        C 4  hhds.  1  gal. 

144000-^-294=489  S&  galls.    J     s<  £489f  gals. 

VIII.  To  measure  planks  or  boards  of  equal  breadth. 
RULE.  Multiply  the  length   by  the  width,  the  product 
will  be  the  contents. 

EXAMPLES. 

14.  What  will  a  hoard  measure  which  is  18  feet  long 
and  1  2  in.  wide  ? 

18  0=length. 
1  2=widlh. 


feet  21    .  .=contents.  Ans.  21  feet. 

15.  What  are  the  contents  of  a  plank  24  6  in.  long  and 
1    1 1  in.  wide  ?  Ans.  46  1 1  in.  6  parts. 

NOTE.  If  the  plank  or  board  is  tapering,  add  the  width  of  both 
ends  together  and  take  half  the  sum  for  the  mean  width,  which  mul- 
tiplied by  the  length  will  give  the  contents. 

IX.  To  measure  scantling  or  small  square  timber. 
RULE.     Multiply  the   width  by  the  thickness  and  their 
product  by  the  length,  the  last  product  will  be  the  contents. 
EXAMPLE. 

16.  What  are  the  contents  of  apiece  of  scantling  18  4  in. 
long,  1  9  in.  broad  and  6$  in.  thick  ? 

Ans.  17  f.  4  in.  6  6  parts. 


DUODECIMALS. 

X.     To  measure  ivood. 

RULE.  Multiply  the  length,  breadth  and  height  contiuu 
ally  together,  and  divide  the  product  hy  123,  the  quotient 
will  be  cords  ;  or  divide  the  solid  feet  by  1C. 
NOTE.     128  feet  make  a  cord  of  wood  or  bark. 

EXAMPLE. 

17.  If  a  load  of  wood  is  7  9  in.  long  ;  3  G  in.  wide  and 
4  10  in.  high ;  how  much  does  the  load  contain  ? 

7     9=lenght»     Or,  16)131  1  3(8  ft,=leord3  1  3  pts, 
3     6= width.  128 

23     3  3 

3  10  G 


27     1   G 
4  10     =height. 

108     6  0 

22     7  3 

128)131      1   3(1   3  1'  3". 

128 

3  Ans.  1  cord,  3  ft.  1  and  3  parts, 

XI.  To  measure  stone  walls  of  cellars,  fyc.  which  are  laid 

by  the  perch  of  24%  cubic  feet. 

RULE.  Multiply  the  length,  height  and  thickness  of  the 
wall  continually  together,  the  product  divided  by  24|  will 
give  the  number  of  perches. 

EXAMPLE. 

18.  A  cellar  wall  is  8  feet  high,  2|  feet  thick,  and  the 
sides  and  ends  together  130  8  in.  long  :  how  many  perches 
are  in  the  wall  ? 

2  9=thickness. 
8     ^height. 

22  0 
130  8r=length. 


242=99)11498  8(116  ^  rods.  Ans.  116^  rods. 


1 20  DUODECIMALS, 

XII.     To  measure  drains,  vaults,  dikes,  cellars,  $c. 
RULE.     Multiply  (be  length,  width  and  depth  in  feet  to- 
gether and  divide  by  2 1C. 

NOTE.     Diggers  work  by  the  square  of  6  feet  long,  wide  and  deep 
.making  .'JIG  cubic  feet  to  a  square. 

EXAMPLES. 

19.  There  is  a  drain  200  feet  long,  3£  feet  wide  and  54 
t'eet  deep  5  how  many  squares  does  it  contain  ? 

Aus.  18|~3-^  sqnares. 

20.  How  many  squares  are  in  a  vault  8  feet  square  and 
9\  feet  deep  ?  Ans.  2|f  squares. 

XII.     To  measure  bales,  trunks,  chests,  S[c.  ;  to  ascertain 
t'^eir  freight,  which  is  commonly  paid  by  the  solid  foot,  or 
so  much  per  tan  of  40  feet. 
RULE.     Find  the  solid  contents  as  before  and  divide  by 

40,  the  quotient  will  be  the  tons. 

EXAMPLES. 

':!i.   What  is  the  freight  of  5  hales  of  goods,  each  meas- 
.ni}£   1  C  in.  Iou?j,3  9  in.  wide  and  2  10  in.  thick,   at 
per !an  ? 

4     8=Iength. 
9=width. 


17     6 
2  10=lhicknesst 


35     0 
14     7 

49     7 

5=number  bales. 


40)247  tl(6¥V  and  1 1  parts  Ans.  $20,14,3, 

22.  How  many  cubic  feet  are  in  10  trunks,  each  meastir- 
£  4  2  in.  long  ;  2  feet  wide  and  1   7  in.  deep  ? 

Ans.  131   11  in.  4  parts. 


-f  NGLE  RULE  OF  THREE  DIRECT. 


SINGLE  RULE  OF  THREE  DIRECT. 

THE  Rule  of  Three  Direct  teaches  by  three  numbers  giv- 
en to  find  a  fourth,  which  shall  have  the  same  proportion 
to  the  third,  as  the  second  has  to  the  first. 

AVhen  more  requires  more,  or  less  requires  less,  the 
question  belongs  to  the  Rule  of  Three  Direct. 

More  requiring  more  is  when  the  third  term  is  greater 
than  the  first,  and  requires  the  fourth  to  be  greater  than 
the  second. 

Less  requiring  less  is  when  the  third  term  is  less  than 
the  first  and  requires  the  fourth  to  be  less  than  the  second. 

Two  of  the  given  terms  are  called  the  "  terms  of  suppo 
stfiow,"  and  one  the   "  demand,"    or  the   number  which 
asks  the  question* 

The  terms  of  supposition  have  "  if"  before  them,  ami 
the  words  "  what  cost  ?"  "  what  will  r"  "  how  much  r' 
"  how  many  ?''  «  how  long  r"  "  how  far  ?"  &c.  are  the 
terms  which  ask  the  question* 

RULE  TO  STATE  THE  QUESTION. 

Write  that  number  which  asks  the  question  in  the  third 
place  ;  that  number  which  is  of  the  same  name  with  the 
one  that  asks  the  question  must  be  put  in  the  first  place; 
that  number,  which  is  of  the  same  name  with  the  answer 
required,  in  the  second  or  middle  place. 

GENERAL  RULE  TO  WORK  THE  QUESTION. 

Multiply  the  second  and  third  numbers  together,  and  di- 
vide the  product  by  the  first,  the  quotient  will  be  the  an- 
swer in  the  same  denomination  with  the  second  or  middle 
term. 

PROOF.     Invert  the  question,  that  i~«,  put  the  fourth  number  or 
answer  in  the  first  place  ;  the  third  number  in  the  second  ;  and  thr- 
second  in  the  third  ;  work  as  before   directed,  and  the  quolicu'. 
be  the  first  number. 


-SINGLE  RULE  OF  THREE  DIRECT. 


EXAMPLES. 

1.  If  8  yards  of  cloth  cost  $4  ;  what  will  24  yards  cost  f 

'\st  term.  2d  term.  3d  term. 

yds.  $.          yds. 

*       :      4    :    :  24 

4=2d.  term, 

1st.  term  8)96 

$12=4th.  term  and  answer.  Ans.  $12. 

NOTE.  In  this  example,  the  first  and  third  terms  are  of  the  same 
name,  viz.  yards,  which  must  always  be  the  case  in  stating  questions 
::i  the  Rule  of  Three  ;  the  fourth  term  or  answer  is  of  the  same  name 
with  the  middle  or  second  term,  viz.  dollars  ;  this  also  must  always 
be  the  case  in  the  Rule  of  Three. 

Proof. 

2.  If  12$  will  buy  24  yards;  how  many  yards  will  $4  burr 

$.  yds.       $. 

12  :  24  :  :  4 

4 

12)96 

yards  8  Ans.  Ans.  8  yds 

Protf. 

3.  If  24  yards  cost  $12  5  what  will  3  yards  eost  ? 

yds.    $.         yds. 

24  :  12  :  :  8 

8 

24)96(48  Ans, 
96 

0  Ans.  $4. 

Proof. 

4.  If  j£4  will  buy  8  yards;  how  many  yds.  will  $12  buy  ? 

$.    yd*.      .  $. 

4:8:  :  12 

8 

4)96 
24  yds,  Ans>  Ans,  24  yds. 


SINGLE  RULE  OF  THREE  DIRECT. 

The  three  methods  of  proof  are  only  the  first  question  varied,  and 
they  will  show  how  any  question  in  this  rule  may  be  inverted. 

A  short  and  easy  method  of  performing  questions  in  the  Single 
Rule  of  Three  is  by  comparing  the  three  given  numbers  together  ; 
the  true  answer  will  result  from  the  nature  of  proportion ;  for  as  much 
greater  or  less  as  the  third  term  is  than  the  first ;  so  much  greater  or 
less  will  the  fourth  term  or  answer  be  than  the  second.  Thus  in  ex- 

yds.  $.         yds. 

ample  1st.  8:4  :  :  24  ;  by  comparing  the  third  term  (24)  with  the 
first  term  (3),  it  will  be  found  to  be  three  times  greater  than  it ;  there- 
fore, the  fourth  term  or  answer  must,  from  the  nature  of  proportion, 
be  3  times  greater  than  the  second  term  (4),  which  is  12,  ajftd  the 
true  answer,  as  by  the  operation  above. 

OBSERVATION  I. 

When  the  second  number  is  of  different  denominations, 
it  must  always  be  reduced  to  the  lowest  mentioned  in  it ; 
then  multiply  and  divide  as  in  the  general  rule,  and  the 
quotient  will  be  the  answer  in  the  same  denomination  to 
which  the  second  was  reduced,  and  which  should  be  brought 
into  the  highest  for  the  answer. 

EXAMPLE. 

5.  If  8  yards  cost  £34  12  6£  ;  what  will  32  yards  cost  ? 
yards.  £,.    s.    d.  qrs.    yds. 

8  :  34  12  6  i  :  :  32  4)132968=farthin<*&. 

20  

12)  33242=pence, 

2,0)     277,0  2 
£138  10  2, 


33242=farthings, 
32 

66484 
99726 

8)1063744=farthings. 

132968=farthings  Ans.  Ans.  £138  10  2. 

NOTE.  In  example  5,  the  second  term  being  in  pounds,  shillings, 
pence  a^id  farthings,  is  reduced  to  the  lowest  mentioned  in  it ;  viz. 
farthings  ;  consequently  the  fourth  ...na  will  be  farthings,  which  are 
reduced  to  pounds  &c.  for  the  answer, 


18* 


SINGLE  RULE  OF  THREE  DIRECT, 


OBSERVATION  II. 

When  the  first  and  third  numbers  are  of  different  de- 
nominations, they  must  be  reduced  to  the  lowest  mentioned 
in  either  of  them ;  then  proceed  as  directed  in  the  general 
rule. 

EXAMPLES. 
6.  If  7  Ib.  sugar  cost  $1,75 ;  what  will  7  2  14  Ib.  cost  r 

lb.     $.  cwt.  qrs.  Ib. 

7  :  1,75  :  :  7  2  14 
4 


7)1494,50 

$213,50  Ans.  g213,56, 

NOTE.  The  first  numbers  being  pounds  weight,  the  third  number  is 
reduced  to  pounds. 

7.  If  7  2  14  Ib.  cost  $213,50  ;  what  will  7  Ib.  cost  ? 

Ans.  $1,75* 

'     OBSERVATION  III. 

When  there  is  a  remainder  after  division,  which  is  of 
the  same  name  with  the  second  term,  reduce  it  to  the  next 
lower  denomination  and  divide  as  before  ;  continue  thus 
till  it  is  reduced  to  its  lowest  denomination,  each  time  di- 
viding by  the  first  term.  Should  there  be  a  remainder, 
place  it  above  the  divisor,  and  annex  the  fraction  thus 
formed  to  the  quotient,  observing  first  to  reduce  it  to  its 
lowest  terms* 


SINGLE  RULE  OF  THREE  DIRECT. 

EXAMPLES. 

8.  If  7  02.  of  gold  is   worth  £30,  or  $30  j  what  will   a 
golden  vase  cost,  which  weighs  7  1 1  oz.  ? 

oz.      £.          Ib.  os.  os.    $.  Ib.  OB. 

7  :  30  :  :  7  1 1  And  7  :  30  :  :  7   1 1 

12  12 

95  95 

30  30 

7)2850  7)2850 


£407  2  IQAi,  $407,1  4,2f. 


9.'  If  7  11  oz.  of  gold  is  worth  $  £407  2  10}  |  ;  what  is 
7  oz.  worth  ?  Ans.  £30. 

10.  If  3  Ib  of  gold  is  worth  £187,  what  is  1  oz.  worth  ? 

Ans.  £5  3  10£  f. 

OBSERVATION  IV. 

When  the  first  term  is  greater  than  the  product  of  the 
second  and  third,  consider  the  product  as  a  remainder  and 
reduce  it  as  directed  iu  Observation  III. 

EXAMPLE.  % 

11.  If  48  yards  cost  £3  or  $3,  what  will  12  yards  cost  r 
yfc.      £,.         yds.  yds.     $.          yds. 

48  :  3  :  :  12  48  :  3  :  :  12 

3  3 


48)36  43)36,00(,75  c. 

20 

4        f!5s. 

48)720(15  s.  "  "[,75  et. 
Here  the  product  of  the  second  and  third  terms  being  less 
than  tne  first  term,  it  is  reduced  to  the  next  lower  denomi- 
nation, giving  15s.   and  75  cents  for  the  quotients  or  an- 
swers. 

OBSERVATION  V. 

When  the  question  will  admit  it,  multiply  and  divide  as 
in  Compound  Multiplication  and  Division. 


SINGLE  RULE  OF  THREE  DIRECT. 


EXAMPLES. 

12.  If  4  yards  cost  £34  10  8£  ;  what  will  12  yds.  cost? 
yds.    £,     t.    d.          yds. 
4  :  34  10  8£  :  :  12 
12 


4)414     8  6 

£103  12  1£  Ans.     Ans.  £103  12  1|. 

13.  If  24  Ib.  cost  £4  8  10£  ;  what  will  96  Ib.  cost  ? 

Ib.    £.  s.    d.  Ib. 

4X0=24.  24  :  4     8  10|  :  :  96 

8  8x12=96. 

35  11     00 
12 


4)426  12 


6)106   13 


£17  15  6  Ans.  £17  15  6. 

OBSERVATION  VI. 

When  the  first  term  happens  to  be  1,  the  operation  is 
performed  by  Compound  Multiplication,  and  when  the 
third  term  is  1,  it  is  performed  by  Compound  Division. 

EXAMPLES. 

14.  If  1  cwt.  cost  £3  15  6i,  or  $12,75  5  what  will  12 
cwt.  cost  ? 

cwt.    £.    s.     d.  cwt. 

1   :  3  15  6|  :  :  12 
12 

£45     6    6  Ans.  5  £45  6  6. 

£$153. 

15.  If  12  cwt.  cost  £45  6  6,  or  $153  5  what  will  1  cwt.  ? 
12)45     66  er  12)153 

£3  15  6*  $~12/75     An(a  $£3  156f 


SINGLE  RULE  OF  THREE  DIRECT. 


Having  stated  all  the  variety  of  cases  which  can  occur  in  the  Rule 
of  Three  Direct  ;  and  furnished  plain  examples  for  their  illustration, 
the  following  promiscuous  questions  are  subjoined  for  the  pupil's  ex- 


Questions. ^Answers. 

16.  If  24  yds.  cost  $0,84,4;  what  will  72  yds.  cost?  $2.53,2, 

17.  108  yds.     .     4,84,6  .     .     ,643yds?     .     29,07,6. 

18.  .     I  cwt.    .     9,00,4  .     .     .  4  2  *14  Ibs.  ?  41,64,3i. 

19.  .    7  Ib.        .       ,38,9  .     .     .  3  cwt.  ?       .     18,67,2". 

20.  .    1  Ib.        .     2,33,4  ...  1  cut.?       .  261.40,8. 

21.  .1  cwt.      261,40,8  .     .     .  1  Ib.  ?          .       2,33,4. 

22.  .    loz.  gold  17,36  ...  1  grain  ?     .         ,03,6£. 

23.  .  3214lb.750,  .     .     .    14  Ib.  ?  .     .     25,86,2/¥ 

24.  What  is  the  interest  of  $874  a  6  per  cent,  for  a  year  ? 

Ans.  $52,44. 

25.  A  bankrupt's  debts  amounted  to   $4800,  and  his  ef- 
fects sold  for  only  $1800  ;  how  much  could  he   pay  on  a 
dollar  ?  Ans.  $0,37,5. 

26.  An  invoice  of  goods  amounted  to  $3480  5  what  is  the 
commission  on  the  purchase  at  3^  per  cent  ? 

Ans.  g!21,80. 

27.  A  bankrupt,  whose  debts  amounted  to   $8749,  com- 
pounded with  his  creditors  for  ,78  cents  on  a  dollar  ;  how 
much  did  he  pay  them  ?  Ans.  $6824,22. 

28.  A  merchant  bought  6  bales  of  cloth,  each  bale  con- 
tained 6  pieces,  and  each  piece  25  yards,  at  $52  per  piece  ; 
what  was  the  value  of  the  whole,  and  what  was  it  worth 
per  yard?  .        5  SI  872  whole. 

ns'l  $2,08  per  yd. 

29.  In  what  time  will  $100  principal  gain  $75,  at  6  per 
cent  per  annum.  ?  Ans.  12£  years. 

30.  A  servant  went  to  market  with  $8,  and  bought  eggs 
at  25  cents  a  doz.  ;  chickens  a  lib  cents  a  pair,  and  ducks 
a  gl  a  pair  ;  he  bought  the  same  number  of  each  kind  ;  how 
many  of  each  sort  had  he  for  his  money  ?      Ans.  4  of  each. 

31.  A  gentleman's  annual  income  amounted  to  $40000  ; 
how  much  can  he  spend   daily,  that  at  the  end  of  the  year 
he  may  lay  up  §25000,  and  distribute  to  the  poor,  quarter- 
ly, $2500  ?  Ans.  13,69,8±f. 

32.  A  merchant  effects  ensurance  on  a  vessel  and  cargo 
valued  at  $18545;  what  is  the  premium  at  44-  per  cent  ? 

Ans.  $834,52,5. 


429  SINGLE  RULE  OF  THREE  DIRECT. 

RULE  OF  THREE  IN  VULGAR  FRACTIONS. 

The  Rule  of  Three  in  Vulgar  Fractions  depends  on  the 
same  principles  as  the  Rule  of  Three  in  whole  numbers. 

GENERAL  RULE. 

1.  Prepare  the  question  as  directed  in  the  Rule  of  Three 
Direct. 

2.  Invert  the  terms  of  the  first  number,  and  multiply  the 
numerate  s  of  the  three  numbers  continually  together  ;  and 
a!)  the  denominators  ;  their  products  will  be  the  answer  to 
the  question. 

EXAMPLES. 
1.  If  |  of  a  yard  cost  £|  ;  what  will  £  of  a  yard  cost  ? 

yds.  £.     yds. 

|=first  number  inverted      r™  o,       8  .  2  .  .  7 
s      .1      j.   «  JL  nen«     -o-  »  -&  •  •  «• 

for  the  divisor. 


niirner.          A   ,   Il2_14_£0  10  41  i 
3X9X8=216  new  denom.        And>  ^6-27-*^ 

Ans  £0  10  41  }. 

2.  If  f  of  a  Ib.  cost  |  of  a  dollar  ;  what  will  -&  of  a  Ib. 
cost  ?  Ans.  /o=ll,  2|  mills. 

OBSERVATION  I. 

When  the  first  and  third  numbers  only  are  fractions  ;  and 

the  second  a  whole  number. 

Reduce  the  first  and  third  to  a  common  denominator,  and 
then  rejecting  the  denominators,  make  the  numerator  of  the 
first,  the  first  number  in  stating  the  question  ;  and  the  nu- 
merator of  the  third,  the  third  number,  and  the  given  whole 
number  the  second  ;  then  proceed  as  in  the  Rule  of  Three 
of  whole  numbers. 

EXAMPLE. 

3.  If  |  of  cwt.  cost  £20  ;  what  will  ^  of  a  cwt.  cost  ? 

6X8=48  \  new  DUm-  H  and  f  f  ,  Then  21  :  20  :  :  48 
7x8=56  common  denom.  48 

<t  <£  _ 

Or,  as  7  :  20  :  :  16  :  45,71,4f.  21)960(45,71,4f. 

Ans,  $45,7  l,4f' 


-<LVGLE  RULE  OF  THREE  DIRECT. 

OBSERVATION  II. 

When  either  the  first  or  third  number  is  an  unit,  and  the 

other  a  fraction. 

RULE.  If  tlie  first  number  is  an  unit,  put  the  denomina- 
tor of  the  fraction  in  its  place,  for  the  first  number,  and  the 
numerator  in  the  place  of  the  fraction  ;  but  if  the  first 
number  is  the  fr  iction,  put  its  numerator  for  the  first  num- 
ber, and  the  denominator  the  third,  proceed  as  in  whole 
numbers. 

EXAMPLES. 

4.  If  a  ship  and  cargo  are  worth  $18400  ;  what  are  J  of 
them  worth  ? 

parts.        $.  parts. 

8  :  18400    :  :  7 

18400x7-7-8=16100 

Ans.  816100. 

5.  Iff  of  a  ship  and  cargo  are  worth  $16100  $  what  ar% 
the  whole  of  them  worth  ? 

parts.        $  parts. 

1  :  16100  :  :  8 

16100X8-7-7=18400. 

Ans.  $18400 

THE  RULE  OF  THREE  /JV  DECIMALS. 

RULE.  Reduce  vulgar  fractions  to  decimals  ;  state  the 
question  and  proceed  as  in  whole  numbers,  pointing  off  as 
in  Multiplication  and  Division  of  Decimals. 

EXAMPLES.       f 

6.  If  £  yard  cost  f  of  a  £,  what  will  }  yd.  cost  ? 

i=:,5.     f=,4.     £=,875, 
yds.    £.          yds.  £. 

Then  as  ,5  :  ,4  :  :  ,875     :     ,700=14$. 

Ans.  14$. 

7.  If  4|  yards  cost  $9,75  ;  what  will  13£  yds.  cost? 

4|=4,5.     13|=13,5. 
yds.        $.  yds. 

Then  4,5  :  9,75  :  :  13,5  :  $29,26  Ans. 

8.  If  8}  yards  cost  $34,90  ;  what  will  43}  yds.  cost  P 
yds-          $.  yds.  $. 

6,625  :  34,90  :  :  43,125  :  174,50.          Ans.gl74,W, 


130  RULE  °F  THREE  INVERSE. 

RULE  OF  THREE  INVERSE. 

THE  Rule  of  Three  Inverse  has  three  numbers  given  to 
find  a  fourth,  which  shall  have  the  same  proportion  to  the 
second,  as  the  first  has  to  the  third. 

When  more  requires  less,  or  less  requires  more,  the  ques- 
tion is  Inverse  proportion. 

More  requiring  less  is  when  the  tlrird  number  is  greater 
'than  the  first  and  requires  the  fourth  to  be  less  than  the 
second. 

Less  requiring  more  is  when  the  third  number  is  less 
than  the  first  and  requires  the  fourth  to  be  greater  than  the 
second. 

GENERAL  RULE. 

State  and  prepare  the  question  as  in  the  Rule  of  Three 
Direct;  multiply  the  first  and  second  numbers  together  for 
a  dividend  and  divide  by  the  third  ;  the  quotient  will  be 
the  answer  in  the  same  name  with  the  second  number. 

NOTE  1.  When  there  are  fractions  in  the  question  proceed  with 
'them  as  in  the  Rule  of  Three  of  Vulgar  Fractions. 

2.  A  knowledge  of  Vulgar  Fractions  is  absolutely  necessary  for  the 
solution  of  many  important  questions  in  the  Rule  of  Three  Inverse  ; 
presuming,  therefore,  that  the  pupil  fully  understands  them,  the  sub- 
sequent questions  are  proposed  for  his  exercise. 

EXAMPLES. 
1.  If  40  men  can  build  a  house  in  180  days  j  how  long 


it  take  80  men  to  build  it  ? 

men.    days.        men.    days. 
40  :   180  :  :  80  :  90 

Ans   90  days. 

NOTE.  Questions  in  this  rule  may  be  performed  in  a  coneise  man" 
aer,  by  comparing  the  third  number  with  the  first  ;  for  as  much  great- 
er or  less  as  the  third  number  is  than  the  first,  so  will  the  fourth  num- 
ber be  less  or  greater  than  the  second. 

2.  If  glOO  principal  in  12  months  will  gain  $6  interest; 
-what  principal  will  gain  the  same  in  6  months  ? 

mo.      <|.          wo. 

12  :  100  :  :  6 

12 


6)1200 
$20§  Ans.  $209. 


DOUBLE  RULE  OF  THREE. 

In  example  2d  the  third  term  is  half  as  much  as  the  first 
and  therefore  requires  the  fourth  to  be  double  the  second  5 
viz.  200  which  is  the  answer. 

3  My  friend  borrowed  of  me  $250  for  3  months,  prom- 
ising me  the  like  favour  ;  soon  after  I  had  occasion  for 
§300  ;  how  long  may  I  keep  it  to  receive  full  compensation 
for  the  kindness  ?  Ans.  2£  months. 

4.  How  much  in   length,  that  is  2|   inches   wide,   will 
make  a  foot  square  ?  Ans.  57|  in. 

5.  How  much  in  length,  that  is   12f   poles  in   breadth, 
will  make  a  square  acre  ?  Ans.  12Tc/y  poles* 

6.  If  3|  yards  of  cloth,  which  is  1£  yd.  wide,  will  make 
a  cloak,  how  much  of  that  sort,  which  is  4  yd.   wide,  will 
make  one  of  tfie  same  size  ?  Ans.  6-^  yds. 

7.  If  a  penny  leaf  of  bread  weighs  7£  oz.  when  flour  is 
10  dollars  per  barrel  ;  how  much  must  the   peucy   loaf 
weigh,  when  flour  is  g!3,50  per  barrel  ?          Ans.  5^-| |  oz. 

8.  If  a  regiment  consisting  of  800   soldiers  were  to  be 
alothed,  each  suit  to  take  3±  yards  of  cloth,  that  is  If  yd. 
wide,  to  be  lined  with  stuff  f-  yard  wide  ;  how  many  yards 
will  it  take  to  line  the  whole  ?  Ans.  4S284  yds 


DOUBLE  RULE  OF  THREE. 

THE  Double  Rule  of  Three  is  commonly  composed  of  Eve 
numbers  to  find  a  sixth,  which  will  bear  the  same  propor- 
tion to  the  fourth  and  fifth,  as  the  third  bears  to  the  first 
and  second,  when  the  proportion  is  Direct. 

If  the  proportion  is  Inverse,  the  sixth  number  will  hear 
the  same  proportion  to  (lie  fourth  and  filth,  as  the  first 
bears  to  the  second  and  third. 

There  are  three  terms  of  supposition,  and  two  which  ask  the  ques- 
tion. The  word  if  precedes  the  terms  of  supposition,  and  the  words 
u  what  will  ?"  "  how  much  rv  "  how  long  ?"  and  the  like,  precede 
the  question. 

PJJLE  TO  STATE  THE  QUESTION. 

1.  Place  the  three  terms  of  supposition  in  this  order  ;  put 
that  number  v.Meii  is  the  cause  of  gain  or  loss,  in  the  first 
place:  that  which  expresses  time,  distance  of  place  and  the 
like,  in  the  second  place ;  and  that  which  is  the  gain  of 
Uss  in  the  third  place. 


DOUBLE  RULE  OF  THREE. 

2.  Place  the  two  numbers  which  ask  the  question  under 
those  of  the  supposition  of  the  same  name  or  kind. 

RULE  TO  WORK  THE  QUESTION. 

1.  If  the  blank  place  fall  under  the  third  term  of  suppo- 
sition, the  question  is  in  Direct  proportion  ;  therefore,  mul- 
tiply the  two  first  terms  together  for  a  divisor,  and  the  oth- 
er three  fora  dividend,  the  quotient  will  be  the  sixth  num- 
ber or  answer. 

2.  If  the  blank  place  fall  under  the  first  or  second  terms 
ef  supposition,  the  question  is  in  Inverse  proportion  ;  then 
multiply  the  first,  second  and  last  terms  together  for  a  div- 
idend, and  the  other  twe  for  a  divisor,  the  quotient  will  be 
the  answer. 

EXAMPLES. 

1.  If  $100  principal  in  12  months  gain  g6  interest  ;  what 
will  $750  principal  gain  in  8  months  ? 

Principal.  Interest. 


mo 


K)0       :     12     :     :     6  750=4th.  terra. 

750     :       8  6=3d.  terra. 

100=lst.  term.  4500 

J2=2d.  term.  8=5th  terra. 

1  200=divisor.  12,00)360,00=dividend. 

830=interesf.       Ans.  $3<l. 

NOTE.  In  the  above  example,  the  blank  place  falls  under  the  third 
term,  therefore  the  proportion  is  direct  ;  the  answer  is  found  by  mul- 
tiplying the  first  and  second  terms  together  for  a  divisor,  and  the  oth- 
er three  for  a  dividend. 

2.  If  glOO  in  12  months  will  gain  $6  interest  :  how  long 
will  it  take  §750  to  gain  $30  interest  ? 

$.  mo.  $. 
100  :  12  :  :  6 
750  3O  Ans.  8  months. 

NOTE.  In  example  2d.  the  blank  falling  under  the  second  term,  thr 
proportion  is  inverse  ;  therefore  multiply  and  divide  by  rule  2d. 

3.  If  16  horses  consume  84  bushels  of  grain  in  21  days  ; 
how  many  bushels  will  suffice  32  horses,  48  days  ? 

Ans.  336  buslr. 


SINGLE  FELLOWSHIP-  133 

4.  If  the  carriage  of  8  hhds.  sugar,  weighing  96  2  14  Ib. 
20     miles,    cost    $40  ;    what   weight   can    he   carried   SO 
miles  for  $120,  at  the  same  rate?  Ans.  193  1  qr=. 

5.  If  12  men,  in  15  days,  can  huild  a  wail  30  feet  long, 
6  feet  high  and  3  feet  thick,  when  the  days  aie   12  hours 
long  ;  in  what  time  will  60  men  build  a  wall  300  feet  long, 
8  feet  high  and  6  feet  thick,  when  they  work  only  8  hours 
each  day  ?  Ans.  120  days. 


SINGLE  FELLOWSHIP. 

FELLOWSHIP  is  a  rule  by  which  merchants,  and  other 
persons  trading  in  copartnership,  so  adjust  their  accounts, 
that  each  may  have  his  share  of  the  gain,  or  sustain  his 
share  of  the  loss,  in  proportion  to  his  capital,  employed  i» 
the  joint  concern. 

The  Affects  of  a  bankrupt  may  also  be  divided  among  his 
creditors,  and  legacies  adjusted  in  case  of  any  deficiency  of 
effects. 

CASE  I. 

When  each  man's  stock,  employed  in  trade,  is  equal. 
RULE.     Divide  the  whole  gain  or  loss  by  the  number  of 
partners,  and  the  quotient  will  be  each  man's  share. 

PROOF.  Add  the  shares  together,  and  their  sum  will  be  equal  to 
the  gain  or  loss.  The  remainders  must  be  reduced  to  the  same  de- 
nomination and  added  together  ;  the  divisor  will  measure  the  sum, 
•which  being  divided,  the  quotient  must  be  added  to  the  particular 
shares. 

EXAMPLE. 

1.  Three  men  entered  into  copartnership  with  equal  con- 
een  in  the  stock;  they  gained  glOOO  j  what  is  each  man's 
•hare  ? 

3)1000=gain. 


333,33,3i=each  man's  share. 

Ans.  $333,33,3^, 


IS* 


134*  DINGLE  FELLOWSHIP, 


CASE  II. 

When  the  several  stocks  are  unequal 

As  the  whole  stock, 

Is  to  the  whole  gain  or  loss  ; 

So  is  each  man's  particular  stock, 

To  his  particular  share  of  the  gain  or  loss. 

EXAMPLES. 

2.  Two  merchants,  A  and  B,  entered  into  trade  ;  A  put 
into  stock  $9740,  and  B  put  in  $8790  jihey  gained  SI874  : 
what  must  each  have  of  the  gain  ? 

$•  gain.         $ 

$9740=A's  stock.  18530  :  1874  :  :  9740— A's  stock. 
8790=B's  stock.  1874 

§18530=whole  stock.  38960 

68180 

77920 
9740 


1853,0)1825276,0(985,03,8TYjV 
$•         g«in-  $•  A's  share. 

18530  :  1874-  :  :  8780  B's  stock. 
8790 

168660 
13118 
14992 


1853,0)1647246,0(888,96,11111.  B's  share. 

A        CA's  share  $985,03,8Ty/3« 
9<  I  B's  share  $888,96,1  jfff 


3.  Three  shipwrights  built  a  vessel  for  g!5500  :  A  ad- 
yanced  $4000,  B  $7000  and  C   g4500 ;  the  ship  sold  for 
£14850  only  5  what  must  each  sustain  of  the  loss  ? 

f.Vs$167,74,lff 

.      Ans.   <  B's  £293,54,8if . 

tC's  $188,70,9ff 

4.  A  merchant  failing  in  business,  owes  to  four  creditors 
as  follows  5  vi>  to  A  £135  10  6,  to  B  £145,  to  C  £154  9 


DOUBLE  FELLOWSHIP,  135 

and  to  1)  £160;  the  value  of  his  effects  is  £252  17  6  ; 
what  must  each  creditor  receive  and  how  much  will  each 
have  on  the  pound  ? 

A'S£57   12 
B'*£61    12 
£65  12 
T>'s£G8     0 

8  6T||-¥rf.  on  a  pound. 
5.  A  B  and  C   entered  into  copartnership  ;  A  put  into 
stock   §875,   B   put  in   8987   and  C    put  in  gll90$  they 
gained  $950;  what  must  each  have  of  the  a;ain  ? 


fA's  $272,36, 
Ant.    <  B's  $307,22,4f  Iff , 
(.C's  g370,41,2|f 


DOUBLE  FELLOWSHIP. 

DOUBLE  FELLOWSHIP  i*  Fellowship  with  time,  and  ife 
when  the  stocks  or' partners  are  continued  in  trade  for  une- 
qual times. 

RULE.     Multiply  each  man's  stock  by  the  time  of  its 
continuance  in  trade,  then  say,  as  in  Single  Fellowship* 
As  the  sum  of  all  the  products, 
Is  to  the  whole  gain  or  loss  ; 
So  is  each  man's  particular  product, 
To  his  share  of  the  gain  or  loss. 
PROOF.     As  in  Single  Fellowship. 

EXAMPLES. 

1.  Two  merchants  entered  into  trade  ;  A  put  into  stock 
$2500  for  3  months ;  B  1800  for  5  months;  they   gained 
^875  ;  what  is  each  man's  share  of  the  gain  ? 
2500X3=7500=A'S  product. 
1800x5=9000=B's  product. 

816500=sum  of  products. 

$.  $.  ^s  product. 

As  16500:875:  :  7500  :  397,72,7T3T=A*8  share  of  gai«, 

$.  $.  jB'.v  product. 

A*  16500:  875  :  :  9000  :  477,27,2T8T=B*s  share  of  gain. 


Proof.     A's  share  g397,72,7T\.7   . 
B's  share  g477,27,2T»T.S 


Whole  gain    $875  .  . 


436  SIMPLE  INTEREST- 


2.  Three  merchants  entered  into  copartnership  ;  A  put 
into  stock  £294  14  for  3  months  ;  B  £240  10  for  4  months, 
and  0  £290  for  6  months  ;  they  gaiued  £300  ;  what  is 
each  partner's  share  of  the  gain  ? 

fA's  share    £73  19  2J 
Ans.  4  B  s  share    £80     9  6*  f  ff 
^C's  share  £146  11   2| 


3.  Three  persons  entered  into  trade  for   16  months  ;  A 
at  first  put  into  stock  $7400,  but  at  the  end  of  4   months 
took  out  $2000,  at  the  end  of  12  months  he  put  in  $3000, 
but  at  the  end  of  14  months  took  out  §850;  B  at  first  put 
in  $5900  and  at  the  end  of  3  months   put  in   $4300  more, 
but  at  the  end  of  9  months  took  out  §40t)0  and  at  the  end  of 
12   months  'put  in  $1500,  but  withdrew  $2000  at  the  end  of 
14  months  ;  C  at  first  put  in  SI  2000,  hut  at  the  end  of  6 
months  took  out  5000,  and  at   the  end  of  9^  months  put  i» 
§3200,  but  at  the  end  of  12  months  took  out  $4000  ;  they 
gained  §8000  ;  what  must  each  partner  have  of  ihe  gain? 

f  A's  share  $2219,39,5|fif. 

Ans.    <  B's  share.  $2634,87,Og\YT- 

tC's  share  $3145,73,3ff4£. 

4.  Three  persons  were  concerned  in  an  adventure  ;  A  ad- 
vanced $4740  for  5   months  ;  B  §2700  for  6  months  ;  C 
§4100  for  4  months  ;  by  miscalculations  and  failures  they 
were  involved  to  the  amount  of  §1800  ;  what  must  each  sus- 
tain of  the  loss  ? 

f  A's  logs  §757,72,6Hf. 

Ans.   «  B's  loss  §517,93,9f£f. 

lC'sloss§524,33,3ff|. 


SIMPLE  INTEREST  IN  FEDERAL  MONET. 

INTEREST  is  a  premium  allowed  for  the  use  of  money. 

Simple  Interest  is  that  which  arises  from  the  principal 
•nly  ;  and  both  the  interest  and  principal  are  always  the 
same  as  at  first. 

1.  Principal  is  the  money  lent. 

2.  The  rate  per  cent,  per  annum,  or  the  ratio,  is  the 
>H  <n  per  cent   agreed  upon,  to  be  paid   for  every   glOO,  ol 
£,  for  the  use  of  the  principal  one  year. 

3.  Amount  is  the  principal  and  interest  added  together. 


SIMPLE  INTEREST.  137 


l&e  rules  of  Simple  Interest  will  apply  also  to  Commission,  Fac- 
torage, Brokerage,  Buying  and  Selling  Stocks,  Ensurance,  and  t*  auy 
tting  else,  rated  at  so  much  per  cent. 


GENERAL  RULE. 

Multiply  the  principal  by  the  rate  per  cent,  and  eiit  oft' 
two  right  hand  figures  i«  the  dollars  ;  if  parts  of  a  dollar 
are  given,  cut  oft'  as  in  the  given  principal. 

CASE  I. 

To  find  the  interest  for  dollars  only,  for  a  year. 

&ULE.  Multiply  the  principal  by  the  rate  per  cent,  and 
•ut  oft*  the  two  right  hand  figures  for  cents,  the  left  hand 
figures  will  be  dollars. 

EXAMPLES. 

i.  What  is  the  interest  of  $474  a  6  per  cent,  per  annum  ? 
$474=principal. 
6=rate  per  cent. 

$28,44=interest  for  a  year.  AnS.  $28,44. 

Questions.  Answers, 

2.  What  is  the  interest  $247  a  4*  per  cent  ?  $11,11,5. 

3  ........    879  a  6  per  cent.  ?  .  52,74 

4.     .  *  ......      35  a  21  per  cent.  ?  .  0,96,2$. 

5  ........     149  a  5  per  cent.  ?  .  7,45. 

6  ........  2340  a  4$  per  cent.  ?  .  99,45. 

7.     .     ......    784  a  5|  per  cent.  ?  .  43,90,4. 

9  ........  1135  a  6i  per  cent.  ?  .  70,93,7  J. 

CASE  11. 

To  find  the  interest  of  dollars  and  cents  for  a  year. 

RULE.  Multiply  the  principal  by  the  rate  and  ent  oft" 
four  right  hand  figures  for  Jeeimals  ;  the  left  hand  figures 
will  be  (he  interest  in  dollars,  the  two  first  decimals  will  be 
cents,  the  third  mills,  and  the  other  the  decimal  of  a  mill. 


138  SIMPLE  INTEREST. 

EXAMPLES. 

9.  What  is  the  interest  of  §378,48  a  4  per  cent,  per  annum  r 

378,48=prineipal. 

4=rate  per  cent. 

$15,1392=interest  for  a  year. 

And  $15,13,9,2=Aus.  $15,13,9]^ 

Questions.  ^Answers. 

10.  What  is  the  interest  of  $578,89  a  6  pr.  ct.  ?  $34,73,3f. 

11.  - 988,38  a  5|  pr.  ct.  ?  56,83,1. 

12 34,47  a  4  pr.  ct.  ?       1,37,8|. 

13 175.98  a  6^  pr.  ct.  ?  10,99,8|. 

14.     . 639,73  a  6|  pr.  ct.  ?  43,18,1. 

CASE  III. 

To  find  the  interest  of  dollars,  cents  and  mills  for  a  year. 
RULE.  Multiply  the  principal  by  the  rate  and  cut  off  fiv« 
right  hand  figures  for  decimals ;  the  left  hand  figures  will  be 
dollars,  the  two  first  decimals  cents,  the  third  mills  and  the 
ethers  decimals  of  a  mill. 

EXAMPLES. 

16.  What  is  the  interest  of  $454,37,6  a  6  per  cent.  ? 
454,37 ,6=priucipal. 

6=rate  per  cent. 

g27,26256=interest  for  a  year. 

$27,26,2,56  =  Ans.  &27.26,£. 

Questions.  Jl/ysivers. 

16.  What  is  the  interest  of  $47.30.4  a  5  pr.  ct.  ?  $2.36,8. 

17 734,48,7  a  4|  pr.  ct.  ?  34,88,8. 

13.     ...     .     .     .     .     .     .  874,47,6  a  6  pr.  et.  ?  52,46,8-|. 

19 98,27,3  ft  6^  pr.  ct.  ?    6,14.2. 

.20 433,87,6  a  6f  pr.  ct.  ?  24,29,7. 

21.    .     • 787,34,7  a  lipr.et.?    8,85,7, 

CASE  IV. 

To  find  the  interest,  of  any  sum  for  several  years  and  parts 

of  a  year,  as  months  and  days, 

RULE.  Find  the  interest  of  the  given  sum  for  a  year, 
then  multiply  it  by  the  given  number  of  years,  and  for  the 
months  take  ?he  aliquot  parts  of  a  year,  and,  for  the  days, 
take  the  aliquot  parts  of  a  mouth. 


SIMPLE  INTEREST. 
EXAMPLES. 


139 


22.  What  is  ifee  interest  of  £437,24  for  4  years,  7  months 
and  10  days  at  6  per  cent,  ? 


6 

nion. 
1 
10 
days. 

2 

487,24  =  principal. 
6  =  rate  per  cent 

29,23,44  ^interest  for  one  year. 
4=number  of  years. 

116,93,76=interest  for  4  years. 
14,61,72=iiiterest  for  6  months. 
2,43,62=interest  for  1  month. 
8  1,20=  interest  for  10  days. 

$134,80,3  =interest  for  4  years,  7  mo.  and 
10  days.  Ans.  $134.80,3. 

23.  What  is  the   interest  of  $478,48  for   3  years  at   6 
per  cent.  ?'  Ans.  $86,12,6. 

24.  What  is  the  interest  of  $987,36,3  for  2£  years  at  6 
per  cent.  ?  Ans.  §123,42 

25.  What  is  the  interest  of  $93,46  for  4|  years  at  5£  per 
cent.  ?  Ans.  $22,07,9. 

26.  What  is  the  interest  of  $4840  for  3  years,  4  months 
and  15  days  at  6  per  cent.  ?  Ans.  $980,10. 

CASE  V. 

T<:find  the  interest  for  months  at  6  per  cent. 
RULE.     Multiply  the  principal  by  half  the  number  of 
months  and  cnt  off  as  in  the  general  rule. 

EXAMPLES. 

27.  What  is  the  interest  of  $75,24  for  8  months  at  6  per 
cent.  ? 

75,24=principal. 

4=^  the,  number  of  months. 

$3,00,96= interest  for  8  months.          Ans.  83,00,9$. 

28.  What  is  the  interest  of  $874  for  7  months  ? 

Ans.  $30,5«. 
£9.  What  is  the  interest  of  38,47  for  11  months  ? 

AM.  $2,11  >. 


SIMPLE  INTEREST. 

CASE  VI. 

To  find  the  interest  for  months  and  days  at  6  per  cent. 

RULE.  Multiply  the  principal  by  half  (he  greatest  even 
Dumber  of  months,  and  J  of  the  given  days  and  the  days 
in  the  odd  month  if  any  ;  cut  oft'  one  figure  for  a  decimal, 
and  proceed  as  in  the  general  rule;  observing,  that  in  find- 
ing the  sixth  of  the  days,  the  remainder,  if  any,  is  a  vul- 
gar fraction,  not  a  decimal,  by  which  multiply  as  usual. 

EXAMPLES. 

30.  What  is  the  interest  of  SI 4,24  for  10  months  and  24 
days  ? 

3)10=mo.  14,24  =  principal. 

—  halfmo.=     5,4=£  of  the  days. 

5=halfmo.  

5696 
«)24=days.  7120 

4=sixth  of  days.  76,89,6=interest  10  months  & 

24  days.     Ans.  §0,76,8. 

31.  What  is  the  interest  of  $24,1 7  for  11  months  and   29 
days  ? 

24,17=principal.  |)ll(5=half  even  mo. 

5.9f =i  mo.  &  %  days. 

— 30= days  in  the  odd  mo. 

21753  29=given  days. 

12085  — 

2014=|  6)59 

l,44,61,7  =  int.  for  given  time.      9£-  =  sixth  of  days. 

Ans.  gl, 44,6. 

32.  What  is  the  interest  of  g35  for  7  months  and  19  days  £ 

Ans.  $1.33,5. 

33.  What  is  the  interest  of  $784  for  9  months  and  24  days  ? 

Ans.  £38,4  !,«• 

CASE  VII. 

To  find  the  interest  for  months  at  any  rate  per  cent. 
feuLE.     Multiply  the  principal  by  the   given  number  of 
months,  and  divide  the  product  by  the  rate  i'or  the  urne. 


INTEREST, 


141 

NOTE.  The  rate  for  the  time  is  found  by  dividing  12  by  the  give?: 
rate  per  cent. 

EXAMPLES. 

34.  What  is  the  interest  of  g748  for  8  months  at  6  percent.  ? 
6)12  748=pnncipal. 

8=number  of  months. 

2=rate  for  the  time. 

2)59,84 

29,92=interest  8  months. 

Ans.  £29,9-. 

35.  What  is  the  interest  of  $40  a  4  per  cent,  for  15  months  ? 

Ans.  §2. 

36.  What  is  the  interest  of  §874,  a  5  per  cent,  for  9  months  ? 

Ans.  $32,77.5. 

NOTE.  When  12  cannot  be  divided  without  a  large  decimal,  it  will 
b&  preferable  to  divide  by  the  vulgar  fraction,  as  in  the  following  ex- 
ample. 

37.  What  is  the  interest  of  $874  a  7  per  eeut.  for  9  months  ? 
7)12  874x9X7=55062-7-12=45,88,5. 

14=V2.  Ans.  £45,88,5. 

CASE  VIII. 

To  find  the  interest  for  days  at  6  per  cent. 
RULE.     Multiply  the  principal  by  £  Of  the  days,  and  cut 
off  the  right  hand  figure  for  a  decimal,  and  proceed  as  in 
the  general  rule. 

NOTE.  This  method  of  finding  the  interest  by  multiplying  by  £ 
of  the  days,  is  sufficiently  exact  for  small  sums  ;  but  for  large  sums 
the  variation  from  the  true  answer  will  be  more,  which  may  be  cor- 
rected by  subtracting  from  the  quotient  _L_  part  of  its  amount. 

EXAMPLES. 

38.  What  is  the  interest  of  $94850  a  6  per  cent,  for  45 
days  ? 

6)45  |)94850=principal. 

—  7!=£  days. 

663950 
TV)711,37,5=for  45  days.          47425 

9,74.4=TV  of  quotient.    

$711.37?5=interest  for  45  days= 

$701, 63,1  =true  answer,  Acs.  $701,63.1, 

13 


SIMPLE  INTEREST. 

39.  What  is  the  interest  of  $374  for  120  days  ? 

Ans.  $17,48. 

40.  What  is  the  interest  of  $15  for  75  days  ? 

Ans.  $0,18,7*, 

CASE  IX. 

To  find  the  interest  of  any  sum  for  any  time,  at  6  per  cent. 
RULE.  Divide  the  given  principal  by  2  and  the  quotient 
will  be  the  interest  for  one  month;  multiply  the  interest 
for  one  month  by  the  months  in  the  given  time,  and  point 
oft*  as  directed  in  the  general  rule. 

EXAMPLES. 

•11.  What  is  the  interest  of  $748  for  8  months  ? 
2)748=principal. 

$3,74=interest  for  one  month. 
8=number  of  months. 

$29,92=interest  for  8  months.  Ans.  $29,92. 

42.  What  is  the  interest  of  $475,48,4  for  3  years  and  4 
months  ? 

2)475,48,4  =principal. 

2,37,7,42=interest  for  one  month. 

40=  number  of  months  in  given  lime. 

$95,09,6,80= interest  for  3  years  and  4  months. 

Ans.  $95,09,6. 

43.  What  is  the  interest  of  $37  for  7  months  ? 

Ans.  gl,29,5. 

44.  What  is  the  interest  of  $95,24  for  11£  months  ? 

Ans.  $5,47,6. 

CASE  X. 

When  the  principal  is  lawful  money  to  find  the  interest  in 

federal  money.,  at  6  per  cent. 

RULE  1.     Multiply  the  principal  by   2,  and  cut  off  the 
right  hand  figure,  for  parts  of  a  dollar.     Or, 

2.  The  shillings  in  the  given  pounds  and  shillings  will 
he  the  interest  in  cents.     Or, 

3.  Divide  the  given  principal  by  5. 


SIMPLE  INTEREST.  143 


EXAMPLE. 

45.  What  is  the  interest  of  £225  in  federal  money  ? 
Rule  1.  £225  Rule  2.  £225     Rule  3.  5)225 

2  20  

S45. 

815,0  $45,00 

Ans,  g45. 

CASE  XT. 

To  find  the  interest  on  bonds,  notes  of  hand,  $c.  when  par* 
tial  payments  have  been  made,  or  endorsed  on  them. 

RULE.  1.  Find  the  interest  of  the  given  sum  to  the  first 
payment,  which  either  alone,  or  with  any  preceding  pay- 
ment, if  any,  exceeds  the  interest  due  at  that  time,  and  add 
that  interest  to  the  given  sum. 

2.  From  this  amount  subtract  the  payment  made  at  that 
time  with  the  preceding  payments,  if  any,  and  the  remain- 
der will  form  a  new  priucipal  ;  the  interest  of  which  iind 
and  subtract  as  of  the  first  sum,  and  so  on  till  the  last  pay- 
ment. 

NOTE.  This  mode  of  computing  interest  is  established  by  law  in 
Massachusetts  for  making  up  judgments  on  securities  for  money  draw- 
ing interest,  and  on  which  partial  payments  are  endorsed.  This  mode 
is  the  most  equitable,  because  the  payments  are  applied  to  keep 
down  the  interest,  no  part  of  which,  in  this  method  of  computation, 
forms  any  part  of  the  principal,  drawing  interest. 

EXAMPLE. 

For  value  received  I  promise  (o  pay  Mr.  Thomas  Bor- 
land, or  order,  twelve  hundred  dollars,  with  interest  in  six 
months  from  this  date.  January  1,  1810. 

ANDREW  DUNKIRK. 

On  the  above  note  were  the  following  endorsements  ;  viz.  May  1, 
1816,  received  $130.  July  1,  received  $16.  December  1,  received 
$24.  January  1,  1817,  received  $400.  March  1,  received  $25. 
August  1,  received  $40.  October  1,  received  $100.  December  1, 
received  $200.  Whjt  remained  due  January  1,  1818  ? 


SIMPLE  INTEREST. 


The  given  sum  bearing  interest  from  Jan.  1,  1816     -     -     $1200 
Interest  to  May  1,  1816,  to  the  first  payment  (4  mo.)     -          24 


Amount  $1224 
May  1,  paid  a  sum  exceeding  interest  then  due     -     -     -         130 


Remainder  for  a  HCAT  principal     --------     §1094 

Interest  due  on  $1094  irom  May  1,  to  Jan.  1,  1817  (8  mo.)      43,76 


Amount  $1137,76 

Paid  July  1,  1816,  a  sum  less  than  int.  then  due  $16 

Paid  Decem.  1,  181C,  a  sum  less  than  int.  then  due     $24 
Paid  Jan.  1,  1817  a  sum  exceeding  int.  then  due        $400 

440 


Remainder  for  a  new  principal     -«--.--._      $697,76 
Interest  on  $697,76  from  Jan.  1,  1817  to  March  1  (2  mo.)         6,97,7 


Amount  $704,73,7 
Paid  March  1,  1817,  a  sum  exceeding  int.  then  due  25 


Remainder  for  a  new  principal     -------  §679,73,7 

Interest  on  $679.73,7  from  Marck  1  to  Aug.  1  (5  mo.)  16,99,3 


Amount  $696,73 
Paid  Aug.  1,  1817,  a  sum  exceeding  int.  then  due     .     -          40 


Remainder  for  a  new  principal    --------       $656,73 

Interest  on  $656.73  from  Aug.  1  to  Oct.  1  (2  mo.)  6,56,? 


Amount  $663,29,7 
Paid  Oct.  1,  1817,  a  sum  exceeding  int.  then  due     -     -         100 


Remainder  ,or  a  new  principal     -------.        $563,29,7 

Interest  on  $563,29.7  from  Oct.  1  to  Decem.  1  (2  mo.)  5,63,3 


Amount  $568,93 
Paid  Decem.  1,  a  sum  exceeding  int.  then  due     -     -     -         200 


Remainder  (for  a  new  principal    -------.       $360,93 

Interest  on  $368,93  due  Jan.  1,  1818  from  Dec.  1,  1817  1,84,4 


Balance  due  Jan.  1,  18 18.  $370,77,4 

Ans.  $370,77,4. 


SIMPLE  INTEREST. 
SIMPLE  INTEREST  LY  STERLING  MOXEY. 

CASE  I. 

To  find  the  interest  of  any  sum  for  a  year. 
GENERAL  RULE. 

Multiply  the  principal  by  the  rate,  and  cut  off  two  right 
hand  figures  ;  the  left  hand  figures  will  be  in  the  highest 
denomination  given  ;  the  right  hand  figures  must  be  reduced 
to  the  lowest  denomination,  each  time  cutting  oft'  the  two 
right  hand  figures. 

NOTE.  When  there  are  several  years,  multiply  the  interest  of  one 
year  by  the  given  number  of  years  ;  and  if  parts  of  a  year  are  given, 
as  months  and  days,  work  by  the  aliquot  parts  which  they  make  of  a 
year  or  month,  the  sum  of  the  quotients  will  be  the  answer. 

EXAMPLES. 

I.  What  is  the  interest  of  £394  at  6  per  cent,  per  annum  £ 
£394=prineipal. 
6=rate. 


£23,64=£23  12  9Jf-  Ans.  £23  12  9|  f-. 

2.  What  is  the  interest  of  £379  12  4^  a  5  per  cent.  ? 

Ans.  £18  19  7*. 

3.  What  is  the  interest  of  £434  for  3  years  at  6  per  cent. 
per  annum  ?  Ans.  £78  2  4*. 

4.  What  is  the  interest  of  £994  10  4i   for  2  years  ami 
9  months  a  6  per  cent,  per  annum  ?  Ans.  £164  1   10|. 

5.  What  is  the  interest  of  £978  at  3£  per  cent,  for  Si- 
years  ?  Ans.  £82  10  4£. 

C.  What  is  the  interest  of  £84  10  for  7  months  and  25 
days  a  6  per  cent.  P  Ans.  £3  6  2£. 

CASE  II. 

To  fund  the  interest  in  federal  money  when  the  principal 
given  is  sterling,  at  6  per  cent. 

RULE.  Add  one  third  to  the  principal,  and  multiply  by 
2,  cut  off  one  figure  ;  the  left  hand  figures  will  be  dollars. 
the  right  hand  figures  parts  of  a  dollar;  or  divide  the  sum 
by  5,  or  multiply  it  by  20  the  product  will  be  cents. 

13* 


146  SIMPLE  INTEREST. 

EXAMPLE. 

7.  What  is  the  interest  in  federal  money  of  £456 
ling  ? 

3) 456=sterliri2f  principal. 
152=1  principal. 

608  608 

By  rule  1.       2     By  rule  2.       20        By  rule  3.  5)608 

$121,60  $121,60  gI2l",GO. 

Ans.  $121,60. 

CASE  III. 

To  find  the  interest  for  months  at  6  per  cent. 
RULE.     Multiply  the  principal  by  half  the  given  num- 
ber of  months,  and  cut  off  as  in  the  general  rule. 

EXAMPLES. 

8.  What  is  the  interest  of  £454   at  6  per  cent,  for   10 
months  ? 

£454=prineipal. 

5=4  number  months, 

22,70 

20 

14,00  Ans.  £22  14, 

•J<  What  is  the  interest  of  £38  12  6£  for  11  months  ? 

Ans.  £2  2  5j. 

CASE  IV. 

To  find  the  interest  for  days. 

RULE.  Multiply  the  given  principal  by  the  given  num- 
ber of  days  and  divide  by  6083,  for  6  percent,  (the  number 
of  days  in  which  any  sum  will  double  itself  at  that  rate) 
the  quotient  will  be  the  answer. 

JS'oTE.  To  find  a  divisor  for  any  rate  percent,  multiply  365  by  100 
"and   divide    the   product  by  the  given  rate  ;  thus,  for  6  per  cent- 

365X100-4-6=6083,  ;  for  5  Per  cent-  3S5X  100-7-5=7300  ;  for  7  per 
acnt.  365 X  100-^7=5214,  &c. 

EXAMPLE. 
10.  What  is  the  interest  of  £28  for  210daysa6  perct.  ? 

c?SX21Q=5$80-f-6Q83?=r£0  19  3^      Ans,  £0  19  3|9 


COMMISSION. 

COMMISSION. 

FACTORAGE  AND  BROKERAGE, 

ARE  premiums,  at  so  much  per  cent,  allowed  a  person 
called  a  Correspondent,  Factor  or  Broker,  iui  assisting 
merchants,  and  others,  in  purchasing  and  selling  good*. 

RULE.  Multiply  the  given  sum  by  the  rate  per  cent,  and 
cut  oft' the  two  right  hand  figures  as  in  Simple  Interest. 

EXAMPLES. 

1.  What  is  the  commission  on  the  purchase  of  goods  the 
invoice  of  which  amounts  (o  §870  at  2|  per  cent.  ? 

870X2|=23,92,5.  Ans.  $23,92,5. 

2.  What  is  due  to  my  Factor  for  selling  goods,  valued 
§1 834  at  2^  per  cent.  ?  Ans.  $45,85. 
.    3.   What  is  the  brokerage  on  £774  at  \\  per  cent.  ? 

Ans.  £11   12  2£.. 

4.  What  must  I  allow  my  correspondent  for  selling  goods 
to  the  amount  of  £48450  at  2£  per  cent.  ? 

Ans.  $1 029,56,2^ . 

5.  I  remit  to  my  correspondent  $32840,  with   orders   to 
purchase  goods  for  my  account  5  what  is  the  amount  of  his 
commission  at  2£  per  cent.  ?  Ans.  &800,97,5|f-, 

BUYING  AND  SELLING  STOCKS. 

STOCK  is  a  fund  established  by  government,  or  corporate 
bodies,  the  value  of  which  is  variable  according  to  the  ex- 
igency of  the  times.  The  practice  of  buying  and  selling 
sums  of  money  in  these  funds  is  become  common. 

RULE.  Multiply  the  sum  to  be  purchased  by  the  excess 
above  100,  cut  off  two  right  hand  figures^  as  in  simple  in- 
terest, which  being  added  to  the  given  sum  will  be  the 
amount  of  the  purchase  required.  If  the  value  is  under 
par,  that  is  under  100,  multiply  by  the  rate  per  cent,  and 
cut  off  as  before  directed. 

EXAMPLES. 

1.  What  is  the  pnrchase  of  $14820  bank  stock  of  the 
United  States,  ».127|  per  cent,  ?  Ans,  $18895»5Q. 


LNSURANCE. 

2.  The  3   per  cent.    United   States  stock,  owned  by  tht 
.city  of  New  York,  amounting  to    $840,000  has  been  dis 
posed  of  at  G8|  per  cent.     What  was  the   amount  of  the 
purchase  ?  Ans.  §575400. 

3.  Manhattan  Bank  purchased  New  York  state  loan  of 
SI, 000,000  of  six  per  cent,  stock  at  101  $  per  cent. ;  what 
was  the  amount  of  the  purchase  ?  Ans.  $1012500. 

4.  The  three  per  cent,  deferred  stock  was  worth  69  pel- 
cent,  in  June  1818;  what  is  the  amount  of  $9745  at  thai; 
rate  ?  Aus.  §6724,05, 


ENSUHJ1NCE. 

1.  ENSURANCE,  or  ASSURANCE, is  a  premium  at  so  much 
per  cent,  given  for  the  security  of  making  good  the  loss  of 
ships,  houses,  goods,   &c.  which  may  happen  by  storms, 
fire,  &c. 

2.  The  amount  ensured  is  called  the  principal. 

3.  The  money  paid  for  ensuring  is  called  the  premium. 

4.  The  "  average  loss"  is  10  per  cent. ;  that  is,  if  the 
owner  of  the  property  ensured  suffer  any  loss  or  damage, 
not   exceeding  10  per  cent,  he  bears  it  himself,  and  the  un- 
derwriter or  ensurer  is  free. 

5.  The  k<  Policy"  is  the  instrument,  by  which  the  en- 
surers  oblige  themselves  to   make  good  the  property   en- 
sured, in   consideration  of  a  certain  premium,  at   a  stipu- 
lated rate  per  cent. 

CASE  I. 

To  find  the  premium  for  ensuring  any  swm- 
RULE.     Multiply  the  given  sum   by  the  rate  per  cent, 
and  cut  off  two  right  hand  figures  as  in  Simple  Interest. 

EXAMPLES. 

1.  What  is  the  premium  on  the  amount  of  a  ship   and 
cargo,  valued  $4844  a  3J  per  cent.  ?  Ans.  $169,54, 

2.  What  is  the  premium  on  a   ship   and  cargo  valued 
$19330  at  3|  per  cent,  from  Boston  to  London,  and  2|  per 
cent,  from  London  to  Boston  r  Ans.  gl  159,80, 


ENSURANCE. 

CASE  II. 
To  find  the   sum  for  which  a  policy  should  betaken  out  to 

cover  a  given  sum. 

RULE.     Subtract  the  premium  from  100,  and  then   say, 
by  the  Rule  of  Three, 

As  the  remainder,  is  to  100  ; 
So  is  the  sum  adventured,  to  the  policy. 
Or  subtract  the  premium  from    100;  annex  two  ciphers  to 
the  sum  to  he  covered,  which  divided  by  the  remainder,  the 
quotient  will  be  the  answer 

EXAMPLE. 

3.  A  merchant  wishes  to  ensure  his  vessel  and   cargo, 
valued  at  $44350  en  a  voyage  to  the  East  Indies;   for  what 
sum  must  the  policy  be  taken  out  to  cover  his  property,  at 
10  per  cent.? 

100 
10=premium  per  cent. 

Remainder    90  :  100  :  :  44350  :  49277,77,7*. 
Or     100 
10 

9,0)443500,0 

49277j77,7*.  Ans.  Ans.  §49277,77,7*. 

CASE  III. 

To  find  the  premium,  when  a  policy  is  taken  out  for  a  cer- 
tain sum,  to  cover  a  given  sum. 
RULE.     As  the  policy,  is  to  the  covered  sum  ; 
3o  is  100,  to  a  fourth  number,  which 
Subtracted  from  100,  the  remainder  will 
be  the  premium. 

EXAMPLE. 

4.  If  a  policy  is   taken   out  for  $49277,77,7*  to  cover 
$44350  what  is  the  premium  per  cent.  ? 

49277,77,7*  :  44350  :  :   100  :  90—100=10. 

Ans.  10  per  cent. 
CASE  IV. 
Having  the  policy  for  covering  any  sum  and  the  premium 

given>  to  find  the  sum  to  be  covered. 
RULE.  Subtract  the  premium  from   100  ;  multiply   the 
policy  by  the   remainder  and  cut   off  the  two  right  hand 
figures,  the  left  hand  figures  will  be  the  sum  to  be  covered, 


150  COMPOUND  INTEREST. 


EXAMPLE. 

5.  If  a  policy  is  filled  for  §49277,77,7^  at  10  per  cent. ; 
what  is  the  sum  to  be  covered  ? 

100  49277,77,7^ 

10==premium.  90 

90=reniainder.      44350,00,00,0      Ans.  $44350. 


COMPOUND  INTEREST. 

.  COMPOUND  INTEREST  is  that  which  arises  from  the  prin- 
cipal and  its  simple  interest,  when  due  and  forborn,  reckoned 
together  as  a  new  sum  ;  so  that  the  principal  and  interest 
is  always  increasing. 

RULE.  Find  the  amount  for  the  first  year,  and  make  it 
the  principal  for  the  second  year  ;  and  so  on  for  any  num- 
ber of  years;  subtract  the  given  principal  from  the  last 
amount,  the  remainder  will  be  the  compound  interest. 

EXAMPLES. 

I.  What  is  the  compound  interest  of  $744  forborn  4 
years  at  6  per  cent,  per  annum  ? 

$744=prinoipaJ.  g835,95,84=prin.  3d  year. 

6=rate  per  cent.  6 

44,64=int.  for  1  year.     50,1 5,7 504=int.  for  3d.  yr. 
744,.  .  =giveii  prin.          835,95,34  . .  =last  principal, 

g788,64=amt.  lst.yr.&>  $886,1  l,5904=amt.  3d.  yr.  & 
6      prin.  2d.  yr.  }  6     principal  4th. 

47,31, 84=int.  2d.  yr.         53,16,695424=int.  4th  yr. 
788,64  . .  =last  prin.          886,1 1 ,5904  .  .=last  principal. 

$835,95,84=auit,  2d.  &     $939,28285824=amt.  4th.  year, 
prin.  3d.  yr.     744 =rgiven  principal. 

$195.28.2?85824=int.  for  4  years. 
Ans,  $195,28.2. 


COMPOUND  INTEREST. 


151 


2.  What  is  the  compound  interest  of  §840  for  3  year?,  at 
5  per  cent,  per  annum    ?  Ans.  g!32,40,5. 

3.  What  is  the  amount  of  £256  10  for  7  year§  at  6  per 
cent,  per  annum  com.  inter.  ?  Ans.  £385  13  7^. 

A  TABLE 

Showing  the  amount  of  l£  or  Ig/rom  i  to  10  years,  at 
4,  4 1,  5,  and  6  per  cent,  per  annum  compound  interest. 


Fears. 

4  |?er  cew£. 

4$  per  cent  A 

5  per  cent. 

6  per  cent. 

1 

2 

3 

4 
5 

1,040000 
1,081600 
1,124864 
1,169859 
1,216653 

1,045000 
,092025 
,141166 
,192519 
,246182 

1,050000 
1,102500 
,15762'5 
,215506 
,276282 

,060000 
,123600 
,191016 
,262477 
.338226 

6 
7 
8 
9 
10 

1,265319 
1,315932 
1,368569 
1,423312 
1,480244 

,302260 
,360862 
,422101 
,486095 
,552969 

,340096 
,407100 
,477455 
,551  328 
,628895 

,418519 
,503630 
,593848 
,689479 
,790848  ; 

NOTE.  The  ratio,  that  is,  the  amount  of  1$  or  1£  for  one  year,  at 
any  eiven  rate  is  thus  found  ; 

$  $  $ 

RULE.     As  TOO  :  104    :  :    1  :  1,04  for  the  first  year. 

100  :  104  :  :  1,04 :  1,0816  for  the  second  year. 
100  :  104  ::  1,0816  :  1,124864  for  the  third  year;  and 
so  for  any  number  of  years,  at  any  rate  per  cent. 

EXAMPLES. 

4.  What  is  the  amount  of  g225  for  3  years  a  5  per  cent, 
per  annum,  compound  interest  ? 

225X1, 157625=260,465625=Ans.  $260,46,5. 

5.  What  is  tke  compound  interest  of  $870  for   8    years 
a  6  per  cent  per  annum  ? 

1,593848x870=1386.647760— 870=Ans.  §516,64,7,, 

6.  What  is  the   amount  of  £845  12  for  9  years,   at  4^ 
per  cent,  per  annum  compound  interest  ? 

845,6X1,486095=1256,641932=:£1256   12  10  Ans. 

NOTE.  The  operation  by  the  common  rule  to  find  the  compound 
interest  of  any  sum  for  several  years  being  extremely  laborious,  the 
preceding:  table  will  greatly  facilitate  tho  work. 


DISCOUNT. 


DISCOUNT. 


DISCOUNT  is  an  abatement  of  part  of  a  sum  of  money. 
due  some  time  hence,  in  consideration  of  prompt  pay,  or 
present  payment  of  the  remainder. 

The  sum  paid  is  the  present  worth,  which  is  such  a  sum, 
as,  if  put  on  interest,  would  in  the  same  time  and  at  the 
same  rate,  for  which  the  discount  is  to  be  made,  amount  to 
the  sum  or  debt  then  due. 

CASE  I. 

To  find  the  discount.  , 

RULE.  As  100  with  its  interest  for  the  given  rate  &  time, 
Is  to  that  interest  ; 
So  is  the  giv.-n  sum, 
To  the  discount  required. 

EXAMPLE. 

1.  What  is  the  discount  of  &84G  for  six  months  at  6  per 
cent.  ? 

$        $          $         $ 
100  103  :  3  :  :  846  :  24,64^. 

6 

mo.       •• 
6U)6,00 

$3  •  r  Ans.  $24,64. 

NOTE.     From  the  given  sum  $846 

Subtract  the   discount  24,64T£7 

Remains  the  present  worth 


CASE  II. 

To  find  the  present  worth. 

RULE.  As  100,  with  the  interest  for  the  given  rate  &  time. 
Is  to  100  ; 
So  is  the  given  sum,  to  the  present  worth. 


DISCOUNT. 

EXAMPLE. 

2.  What  is  the  present  worth  of  &874  at  6  per  cent,  due 
4  years  hence  ? 

$         $  $          $ 

100  124  :  100  :  :  874  :  701,83,8  ff. 

6 

6,00 

#r* 

24=Int.  for  4  years.  Ans.  $704,83,8f  f . 

NOTE.     From  the  given  sum          874 

Take  the  present  worth   704,83,8|f 

Remains  the  discount    $169, 16,1  ^T 

NOTE  1.  It  is  immaterial  whether  the  present  worth,  or  the  dis- 
count is  first  found,  for  the  difference  between  the  debt  and  either  of 
them  will  be  the  other. 

2.  The  general  practice  among  bankers  in  discounting  bills  is  to 
find  the  interest  of  the  sura  drawn  for,  from  the  time  the  bill  is  dis- 
counted, to  the  time  when  it  becomes  due,   including  the  days  of 
grace  ;  which  interest  is  reckoned  as  the  discount.     This  method, 
Jiowever,  makes  the  Discount  more  than  in  justice  it  would  be. 

BANK  DISCOUNT. 

RULE.  Multiply  the  given  sun?  by  £  of  the  days,  in- 
cluding the  days  of  grace,  and  cut  off'  as  directed  in  Case 
VIII.  in  Simple  Interest,  Federal  Money. 

EXAMPLES. 

3.  What  is  the  discount  of  $1 1540  for  30  days  ? 

11540  i)33=given  days  with  grace. 

5 1  &i=A  days  and  grace. 

57700 
5770 


$63,47,0  Ans.  §63,47, 

4.   What  is  the  discount  of  §12000  for  60  days  ? 
i)63=given  days  uith  grace.  12000 


=£  days  and  grace. 


120000 
6000 


Ans- 
14 


EQUATION  OF  PAYMENTS— BARTER. 

In  the  preceding  examples  for  30  and  60  days,  the  3 
jlays  of  grace  are  added,  making  33  and  63  days,  which  is 
the  customary  mode  at  the  banks. 


EQUATION  OF  PAYMENTS. 

EQUATION  o?  PAYMENTS  is  finding  a  meantime  for  pay- 
ing the  whole  debt,  when  several  sums  are  due  at  different 
times. 

RULE.  Multiply  each  sum  by  its  time  of  payment,  and 
divide  the  sum  of  the  products  by  the  whole  debt ;  the  quo- 
tient will  be  the  equated  time. 

EXAMPLES. 

I.  A  owes  B  $2000,  of  which  $500  is  to  be  paid  in  4 
jnonths  ;  £600  in  5  months  ;  $600  in  6  months  ;  and  $300 
in  8  months  ;  when  must  the  whole  be  paid  at  one  pavment  ? 

500X4=2000 
600x5=3000 
600x6=3600 
300X8=2400 


The  whole  debt      2,000)  1 1 ,000=sums  of  products. 

5i  mo.         Ans.  5£  months. 

2.  A  merchant  bought  goods  to  the  value  of  $4000,  to 
be  paid  as  follows;  -viz.  $1200  in  4  months  ;   g800  in  6 
months,  and  the  remainder  in  12  months;  but  afterwards 
agreed  to  pay  the  whole  at  ane  time ;  when  must  the  debt 
be  paid  ?  Ans.  8  mo.  12  days. 

3.  A  owes  B  $840  to  he  paid  as  follows  :  1  in  3  months, 
^  in  4  months,   and  the  rest  in  6  months;   at  what  time 
must  the  whole  be  paid  at  once  ?  Aus.  4J  months. 


BARTER. 

BARTER  is  the  exchanging  of  one  commodity  for  another, 
and  instructs  traders  so  to  proportion  their  goods  of  differ- 
ent kinds,  value  and  quantities,  that  neither  party  may  sus- 
tain loss. 


BARTER. 

CASE  I. 
When  the  quantity  and  value  of  one  article  are  give}L,  to  find 

how  much  of  some  other  must  be  given  for  it. 
RULE.     Find  the  value  of  that  article,  whose  price  is 
given  :  then  say,  by  the  Rule  of  Three  Direct, 

As  the  pricje  of  the  article  required,  per  Ib.  or  yd.  &e. 

Is  to  1  Ib.  1  yd.  &c. ; 

So  is  the  value  of  the  given  article, 

To  the  quantity  of  the  article  required". 

EXAMPLES. 

1.  Two  merchants  barter;  A  has  12  2  14lb.  of  sugar  at 
$12  per  cwt.  which  he  wishes  to  exchange  with  B  for  cot- 
lon  at  25  ceuts  per  Ib. :  hovr  much  cotton  must  B  give  A 


for  his  sugar  ? 
qrs.' 


lllb 


12=price  1  cwt.  sugar. 
12 

c.      Ib.  $. 

144         As  ,25  :  1   :  :  151.50 
6  '   1 

1,50  

,25)151,50(606  Ib. 


$151,50=value  of  A's  sugar. 

B  must  give  A  606lb.  cotton  for  l£  2  14lb.  sugar. 

Ans.  6061b. 

2.  A  has  rum  at  Sl;50  per  gal.  and  B  has  4  pipes   of 
Madeira  wine,  containing  125  ga/Tbjis  each?  at  $3,50  p 
gal.  how  much  of  A's  rum  can  B  have  for  his  wine  ?^ 

Ans.  1166|  gals. 

3.  How  much  coffee,  at  23  cents  perlb.  must  be  given  in 
barter  for  9  chests  of  tea,  each  weighing  95  Ib.  at  gl,75 
per  Ib.  ?  Ans.  6505  6  IS^  drs. 

CASE  II. 
When  a  trader  has  goods  at  a  certain  price  ready  money, 

but  in  barter  advances  the  price. 

RULE.  Find  at  what  the  other  ought  to  rate  liis  goods, 
in  proportion  to  that  advance  price ;  then  proceed  as  in 
Case  I. 

J^OTF..  The  quantity  of  the  latter  commodity  maybe  found  either 
by  the  ready  money  or  bartering  price. 

EXAMPLES. 

4.  A  has  raisins  at  25  cents  per  Ib.  ready  money,  but  in 
barter  will  have  30  cents  per  lb.$  B  has  tea  at  $1,75  per 


BARTER. 

Ib.  ready  money  :  what  ought  B  to  rate  his  tea  at  inbarter> 
and  what  quantity  of  tea  must  be  given  for  20  boxes  ot" 
A's  raisins  each  weighing  35  Ib.  ? 

35  700Z6. 

20  ,25  ready  money  price. 

7.00=wt.  of  raisins.  3500 

,30=barter  price.  1400 

$210,00=value  of  raisins,      $175,00  =alue  at,  ready 
at  bartering  price.  money, 

c.  c.  $. 

As  ,25    :    .30    :     :     1,75 
.30 


.25)5250(2,10  B's  bartering  price. 

$  Ib.  $. 

As  2,10     :     1     :     :     210,00 
1 

2, 10)2 10,00(1 00  Ib.  tea. 
Or  ready  money  price. 

$.        ib.     $. 

As  1,75  :  1   :  175,00 
1 

1,75)175,00(100  Ib.  tea  as  before. 

A        fS2,10  B's  barter  price, 
*'  £100lb.  quantity  of  tea. 
PROMISCUOUS  QUESTIONS. 

5.  A  trader  lias  cinnamon  at  30d.  per  Ib.  ready  money, 
iu  barter  must  have  3Qd.  per  Ib. ;  B  has  nutmegs  worth 
;.  per  Ib.  ready  money;  at  how  much  must  B  rate  his 
Tiutmegs  per  Ib.  that  his  profit  may  be  equal  to  A's  ? 

Ans.  9s. 

C.  Two  traders  barter ;  A  has  120  cwt.  sugar  at  $12  per 
,>\t  :  B  has  256  yards  broadcloth  at  $5  per  yard;  who 
must  receive  the  difference,  and  how  much  ? 

Ans.  $160  difference  in  favour  of  A. 
i.  A  has  200  yards  of  broadcloth  worth  g2550  per  yard, 
lor  which  B   gives  him  $250  ready  money,  and   500  gal- 
lons of  molasses ;  at  what  did  B  value  his  molasses  per 
gallon  ?  Ans.  50  cents  per  gaL 


LOSS  ^ND  GAIN. 


157 


'o.  A  has  200  yards  of  broadcloth  worth  $2,50  per  yard,  for 
which  B  gives  him  $250  in  cash,  and  the  rest  in  molasses 
at  50  cents  per  gal. ;  how  much  molasses  did  B  give  A  be- 
sides the  cash  ?  Ans.  500  gals. 

9.  A  exchanges  with  B  40  Ib.  of  indigo  at  gl  per  Ib. 
ready  money,  and  $1,25  in  barter,  but  is  willing  to  lose  10 
per  cent,  to  have  ^  ready  money  ;  what  is  the  ready  money 
price  of  1  yd.   of  cSoth  delivered  by  B  at  S3,50,  to  equa'l 
A's  bartering  price  :  and  hew  many  yards  were  delivered  ? 
A        C$<MMI  ready  money  price  of  1  yd. 
5'£l2f  yards  delivered  by  B. 

NOTE.  The  preceding  may  suffice  to  illustrate  the  most  general 
cases  in  Barter.  Other  questions,  however,  which  may  not  be  con- 
tained in  them,  may  be  easily  answered  by  a  careful  consideration  of 
their  nature. 


LOSS  AND  GALV. 

Loss  AND  GAIN  is  a  rule,  by  which  merchants  and  tra- 
ders know  what  they  gain  in  retailing  goods,  and  in  case 
of  damage,  what  they  lose  by  selling  at  any  given  rate  ^ 
and  whether  they  gain  or  lose,  at  what  rate  per  cent. 

The  gain  or  loss  is  in  proportion  as  the  quantity  of 
goods  ;  therefore  questions  in  this  rule  are  answered  by  the 
Rule  of  Three  Direct. 

CASE  I. 

To  know  what  is  gained  or  lost  per  cent. 
RULE.     1.  See  what  the  gain  or  loss  is  by  Subtraction> 
2.  Say  by  the  Rule  of  Three  Direct, 
As  the  price  it  cost, 
Is  to  the  gain  or  loss ; 
So  is  100,  to  the  gain  or  loss  per  cent. 

EXAMPLES. 

1.  Wheat  is  bought  at  $1,25  and  sold  at  $1,50  per  bushel? 
what  is  the  gain  per  cent,  ? 

$          '-         $ 

$1.50=priee  sold  for.         As  1,25  :  ,25  : :  100,00 
l,25=price  given.  ,25 

j25=gain  per  hush.  l,25)2500,00(20,0a 

Aus.  20  per 
14* 


LOSS  AND 

2.  How  much  per  cent,  profit,  at  4s.  on  the  pound  ? 

Aus.  20  per  cent. 

3.  How  much  per  cent,  profit,  at  25  cents  on  the  dollar  f 

Ans.  25  per  cent. 

CASE  II. 
To  know  how  an  article  must  be  sold  to  gain  or  lose  so 

much  per  cent.  ? 

RULE.     By  the  Rule  of  Three,  say, 
As  100,  is  to  the  price; 

So  is  100,  with  the  gain  added,  or  loss  subtracted, 
To  the  gaining  or  losing  price. 
EXAMPLES. 

4.  If  wheat  is  bought  for  SI, 25  per  bushel ;  how  must  it 
W  sold  to  sain  20  per  cent.  ? 

$•       $>  $ 

100  :  1,25  :   :  120 

120 

$l,50,00=selling  price  per  bush.       Ans.  SI, 50. 

5.  If  goods  worth  §450  are  shipped  and  corne  to  a  bad 
market ;  what  will  be  the  amount,  if  sold  at  15  per  cent. 
loss  ?  Ans.  $382,50. 

6.  Bought  150  yards  cloth  for  £45 ;  how  must  it  be  sold 
to  gain  25  per  cent.  ?  Ans.  £56  5. 

CASE  III. 
To  know  ivhat  an  article  cost,  when  there  is  gained  or  lost 

so  much  per  cent.  ? 
RULE.     By  the  Rule  of  Three,  say, 

As  100  with  the  gain  added,  or  loss  subtracted, 
Is  to  the  price ; 
So  is  100,  to  the  prime  cost. 
EXAMPLES. 

7.  If  wheat  is  sold  for  gl,50  per  bush,  and  there  is  gain- 
^td  20  per  cent. ;  what  did  it  cost  per  bushel  ? 

100 
20 

• $  $ 

120     :     1,50     :     :     100 

1.50 
12,0)15,00,0 

$l,25=;primecost,     Ans,  $1,25. 


EXCHANGE, 

8.  If  goods  are  sold  for  $382,50  ;  by  which  there  is  lost 
15  per  cent, ;  what  was  the  first  cost  of  them  ? 

Ans.  $450. 

CASE  IV. 

To  know  what  would  be  gained  or  lost  per  cent,  if  goods, 
sold  at  such  a  rate,  there  is  gained  or  lost  so  much 

per  cent,  if  sold  at  another  rate. 
RULE.     By  the  Rule  of  Three,  say, 
As  the  first  price, 

Is  to  100,  with  the  gain  added  or  loss  subtracted; 
So  is  the  other  price, 
To  the  gain  or  loss  per  ceiit.  at  the  other  rate. 

NOTE.     If  the  answer  is  100,   there  is  neither  gain  nor  loss  ;  the 
excess  of  100  is  gain  ;  the  deficiency  of  100  is  loss  per  cent. 

EXAMPLES. 

9.  If  wheat,  sold  at  gl.50  per  bushel,  gain  20  per  cent 
what  gain  or  loss  per  cent,  will  there  be  if  sold  at  §1,2-5 
per  bushel  ? 

S-  ?•  $• 

As    1,50     :     120     :     :     1,25 

120 

1,50)150,00 

$100 
Ans.  There  is  neither  gain  nor  loss. 

10.  If,  when  tea  is  sold  at  $1,40  per  Ib.  there  is  lost  30 
per  cent. ;  what  is  the  gain  or  loss  if  it  should  be  sold  at 
$1,50?  Ans.  §25  loss. 


EXCHANGE. 

EXCHANGE,  considered  as  the  subject  of  Arithmetic  is 
the  method  of  finding  how  much  money  in  oce  country  is 
equivalent  to  a  given  sum  in  another. 

"Par"  signifies  equality  ;  that  is,  when  a  sum  of  money 
in  one  country. is  of  the  same  value,  or  contains  the  same 
quantity  of  pure  gold  or  silver  as  a  sum  in  another  coun- 
try ;  Exchange  then  is  said  to  be  at  par. 

"  The  course  of  Exchange"  is  the  current  price  between 
two  places,  which  is  sometimes  above  and  sometimes  below 


|60  EXCHANGE. 

par,  according  to  the  circumstances  of  trade,  or  the  de- 
mands of  money.  The  course  of  Exchange  between  two 
nations  is  figuratively  speaking,  a  herald,  which  proclaims 
publicly  the  state  of  commerce  and  money  negotiation*  be- 
twixt them,  and  which  of  the  two  is  indebted  to  the  other. 

Questions  in  Exchange  are  answered  by  the  Rule  of 
Three  or  Practice. 

Rules  for  reducing  the  several  currencies  of  the  United 
States,  also  Canada  ami  Nova-Scotia,  to  a  par  each  with 
the  other,  have  been  given  ;  see  page  92-95. 

The  subsequent  relate  principally  to  foreign  Exchange. 

I.     GREAT  BRITAIN. 

Accounts  are  kept  in  Great  Britain  and  the  West-In- 
dies in  pounds,  shillings,  pence  and  farthings. 

4  Qd.  sterling  is  equal  to  one  dollar  federal  money. 

CASE  I. 

To  change  pounds  sterling  to  federal  money. 
RULE.     To  the  sterling  add  i,  to  the  sum  annex  three 
ciphers,  divide  by  3,  and  cut  off  the  two  right  hand  figures 
for  cents,  the  figures  on  the  left  will  be  dollars. 

EXAMPLE. 

1.  In  j£l26  sterling  how  many  dollars  ? 
£)126=sterling. 
42 

3)168000 


8560,00  Ans.  $560. 

CASE  II. 
To  change  pounds,  shillings,  pence  and  farthings  sterling  te 

dollars  and  cents. 

RULE.  Reduce  the  shillings,  pence  and  farthings  to  the 
decimal  of  a  pound  by  Case  II.  or  III.  in  Decimal  Frac- 
tions, annex  it  to  the  given  pounds,  add  £  of  the  sum,  divide 
by  3  and  cut  off  two  right  hand  figures,  as  before  directed. 

EXAMPLE. 

2.  Reduce  £246  18  4£  sterling  to  federal  money. 
i)246.919 
82306 
3)329225 

$1097,41|  Ans.  $1097,41$, 


EXCHANGE.  J  Q  ± 

CASE  III. 

To  change  dollars  to  sterling. 

RULE.  Multiply  the  dollars  by  3,  from  the  product 
subtract  ^.  and  from  the  remainder  cut  oft'  the  right  hand 
figure  for  the  decimal  of  a  pound. 

EXAMPLE. 

3.  In  $560  how  many  pounds  sterling  ? 
560=given  dollars. 
3 

£)1680 
420 


£126,0  Ans.  £126. 

CASE  IV. 

To  change  dollars  and  cents  to  pounds  sterling. 
RULE.     Multiply  the  dollars  and  cents  by  3,  from  the 
product  subtract  £,  and  from  the  remainder  cut  off  the 
three  right    hand    figures  for  decimals  of  a  pound,  the 
figures  on  the  left  will  be  pounds  sterling. 

EXAMPLE. 

4.  Reduce  $1097,41f  to  sterling. 
3 


82306,25 

£246,91875=£246  18  4£.     Ans,  £246  18  4£, 
II.    IRELAND. 

Accounts  are  kept  in  pounds,  shillings,  pence  and  farth- 
ings. 

4  IQi  qr8f  Iri.sh  are  equal  to  SI  Federal  Money. 
1  l</.Irisli=ls.  sterling;  or  £108  6  8  Irish=£lOO  sterling; 
therefore  in  reducing  sterling  to  Irish  at  par  -*-%  is  added  to 
Sterling:  and  T\  is  subtracted  from  Irish  to  reduce   it  to 
Sterling  Money  at  par. 

CASE  I. 
To  reduce  Irish  to  Federal  Money. 

RULE.  From  the  Irish  Money  subtract  -3^,  the  remain* 
der  will  be  sterling,  which  reduce  to  Federal  Money  by 
case  I.  or  II.  Great-Britain. 


EXCHANGE. 


EXAMPLE. 
1.  In  £108  6  8  Irish  how  much  federal  money  ? 

6  8=lrish. 
868 

0  0=sterling. 

33  6  8 

133  6  8=133,333H-3=444,44|.      Ans.  $444,44' 

CASE  IT. 

To  change  Federal  Money  to  Irish. 
RULE.     Reduce  the  given  8utn  to  sterling,  (by  Case  IV. 
Great-Britain,)  to  which  add  •&>  the  sum  will  be  Irish. 

EXAMPLE. 

&    In  g444,44i  how  much  Irish  money  ? 
444,44i=federal. 
3 

£)1  33333 
33333 

TV)100.000=sterling. 
868 


£108  6  8=Irish.  Ans.  £108  6  8. 

III.    HAMBURGH. 

In  Hamburgh  accounts  are  kept  either  in  Pounds,  Schil- 
lings, and  Groats  Flemish  ;  or  in  Marks,  Schillings  Lubs, 
or  Stivers,  and  Phinnings  or  Deniers. 

12  phinnings,  or  deniers,  or  2  groats=l  schilling-lub,  or  stiver=l  1-8 

penny  sterling. 
16  schillings-lubs,  or  stivers,  or  32  groats=l  mark=l  6d.  sterling, 

2  marks 1  dollar=3j.  sterl. 

3  marks 1  rix  doll.=4  6rf.  ster.=r 

1$  federal  money. 

7f  marks >....!    pound    Flemish. 

"32  Flemish  pence 1  mark. 

ALSC, 
12  groats  or  pence  Flemish     .....      1  schilling  Flemish. 

20  schillings  Flemish 1  pound. 

The  mark  banco=33  1-3  cents  by  the  laws  of  United  States. 

NOTE.     The  current  money  of  Hamburgh  is  of  less  value  than  that 
of  the  Bank.     This  difference  is  called  the  "  as  " 
ble,  but  always  in  favor  of  the  bankv 


EXCHANGE. 

100  Ib.  in  Hamburgh  =  107|  lb<  in  the  United  States. 
100  ells  .        .     .     .     =    62£  yards. 

CASE  I. 

To  reduce  Marks  to  Federal  Money. 
RULE.     Divide  the  given  sura  by  3. 
EXAMPLES. 

1.  Reduce  155442  marks  to  dollars  and  cents,  at  33|  cts. 
per  mark. 

33£=!  of  a  dol.     3)155442=marks. 

g51814  =  dollars. 

Ans.  $51814. 

2.  In  8456  marks  3  stivers  ;  how  many  dollars  and  cts.  ? 

3)8456 =marks. 

2818,06| 

,16f =8  stivers. 

$2818,831  Ans.  $2818,83*. 

CASE  II. 

To  reduce  Federal  Money  to  Marks. 
RULE.  Multiply   the  dollars  by  3,  the  product  will  be 
marks.     If  dollars  and  cents  are  given,  multiply  by  3,  cut 
off  two  right  hand   figures,  for  decimals  of  a  mark,  which 
heing  reduced  will  give  the  stivers  and  deniers. 

EXAMPLE. 

3.  Reduce  $2818,83^  to  marks  and  stivers. 

$28 18,831 
3 

Marks  8456.50 

16  stivers  =  mark. 

300 
50 


Stivers   8,00  Ans.  845G  marks  8  stivers, 

€ASE  III, 

To  reduce  Hamburgh  to  Sterling  Money. 
RULE.     Divide  the  given  sum  by  the  rate  of  Exchange, 
and  the  quotient  will  be  Sterling. 


EXCHANGE. 

EXAMPLE. 

4.  How  much  sterling  will  a  bill  on  Hamburgh,  amount 
ing  to  6609  marks  6  stivers,  be  worth,  Exchange  at  35  3d 
per  pound  sterling  ? 

35  3d.  6609  marks  6  stivers. 

12  32= marks          2 

423  13218  12  groats. 

-19827 

12=6  stivers. 


423)211 5  )0( 500  £.  sterling. 

2115  Ans.  £.  500. 

00 

CASE.  IV. 

To  reduce  Sterling  Money  to  Hamburgh  currency. 
RULE.     Multiply  the  sterling  by  the    rate  of  exchange, 
and  the  product  will  be  the  answer  in  the  same  denomina- 
tion to  which  the  exchange  was  reduced. 

EXAMPLE. 

5.  How  many  marks  should  be  received  at  Hamburgh, 
for  £.500  sterling,  exchange  at  35  3d.  per  pound  sterling-? 
35  3  423 

12  500 

423=groats    2)21 1500=groats. 
16)105750=stivers. 
marks  6609,6     Ans.  6609  marks,  6  stivers. 

NOTE.  To  reduce  current  to  bank  money  ;  say,  as  100  with  the 
agio  added,  is  to  100  bank :  so  is  the  current  money  to  the  bank 
money  required.  Also  to  reduce  bank  into  current  money  ;  say,  as 
100  is  to  100  with  the  agio  added :  so  is  the  bank  money  given,  to 
the  current  required. 

IV.    HOLLAND. 

In  Holland  there  are  two  banks,  the  one  of  Amsterdam  and  the 
other  of  Rotterdam.  The  bank  of  Amsterdam  is  the  most  famous 
and  considerable  in  Europe.  It  was  established  in  1609,  by  the  au- 
thority of  the  States  General,  under  the  direction  of  the  Burgomas- 
ters of  the  city,  who,  having  constituted  themselves  the  perpetual 
cashiers  of  the  merchants  of  Amsterdam,  are  themselves  a  security  for 
the  bank. 


EXCHANGL. 

Various  opinion-  have  been  formed  respecting  the  real  sum  of  mon- 
ey deposited  in  this  bank,  but  very  few  have  estimated  it  under  30 
millions  sterling. 

It  is  to  this  bank  the  city  of  Amsterdam  owe?  its  splendor  r.jul 
magnificence,  which  though  it  possesses  the  greatest  part  of  th<; 
merchants  ready  money,  rather  promotes  than  interrupts  their  com- 
merce, by  the  security  and  dispatch  with  which  a  bank  credit  is  at- 
tended ;  for  as  business  in  the  bank  is  negotiated  by  transfers,  mill- 
ions may  be  paid  in  a  day,  without  the  intervention  of  any  cash, 
which  is  of  the  greatest  consequence  in  expediting  trade  that  can 
possibly  be  imagined.* 

In  Holland,  Flanders  and  Germany,  accounts  are  kept  iu 
Pounds,  Schillings  and  Pence  Flemish,  divided  as  the 
British  pound;  but  they  *re  kept  more  generally  in  Guild- 
ers or  Florins,  Stivers,  Deniers  or  Phiuuings. 

8  Phinnings     .     .     make       .     1  Groat.     .     .        s.  <?. 

2  Groats,  or  16  phinnings       .        Stivtr     .     .        =0  l^V  sterling, 
20  Stivers,  or  40  groats  .     .     .         Guilder,  orllorin=l    1)  ,86  ster. 
12  Groats,  or  6  slivers    .     .     .         Schilling    ..=06  ,56 
20   Schilling?,  or  6  guil.  or  florins      Pound  Flemish  =  10  11  ,18 

2-i-  G  uilders Rix  Dollar     .      =4     6  ,66 

The  guilder  or  florin  of  the  United  Netherlands  is  equal 
to  40  cents  in  the  United  States,  or  2  cents  per  stiver. 

100  Ib.  in  Amsterdam  =  109-}  Ib.  in  the  United  States. 

100  ells  :§=  75  yds.  in  the  United  States. 

Britain  exchanges  with  Holland  on  the  pound  sterling, 
which  is  estimated  a  £.1  16  6  Flemish. 

CASE  I. 

To  reduce  Dutch  mawy,  that  is,  Guilders  or  Fforins  to 

Federal  money. 

RULE.  Multiply  the  guilders  or  florins  by  40,  the  pro- 
duet  \vill  be  the  cents. 

EXAMPLES. 

1.  In  24£0  guilders,  how  much  Federal   money,  at  40 
exchange  per  guilder  ? 
2480  =  guilders. 
40  —  exchange, 

$992,Q.Q  Ans.  £992 

V 
-Jackson, 

15 


166  EXCHANGE. 

2.  Remitted  from  Amsterdam  to  Boston  a  bill  of  1855 
guilders  13  stivers  ;  how  many  dollars  and  cents,  exchange 
at  40  cents  per  guilder  ? 

1355  13  =  stivers. 

40  2 

74200  26  =  cents* 

26 

$742,26  Ans.  $742,26. 

CASE  IT. 

To  reduce  Federal  Money  to  Guilders  or  Florins,  $c. 
KULE.     Divide  the  dollars  and  cents  by  40,  the  quotient 
will  be  guilders:  and  half  the  remainder  will   be  the  sti* 
vers. 

EXAMPLES. 

3.  In  g992,00  how  many  guilders  ? 

4,0)992,0,{) 

2480  =  guilders. 

Ans.  2480  guilders. 

4.  In  $742,26  hew  many  guilders  ? 

4,0)742,2,6 

1855,26  —  1855  guilders  13  stivers. 

Ans.  1855  guil.  13  stivers. 
CASE  III. 

To  reduce  Flemish  to  Sterling. 

RULE.  Divide  the  given  sum  by  the  rate  of  exchange. 
EXAMPLE. 

5.  A  merchant  at  Amsterdam  remits  £876  10  10  Flem- 
ish, to  be   paid  at  London ;    for  how  much  sterling  mon- 
ey must  he  draw,   the  exchange   being  a  33  6d.  Flemish 
per  pound  sterling  ? 

33  6(f.  876   10  10 

12  20 

402  17530 

12 

402)210370(523  6  2F2T  sterling. 

Ans,  £-523  6  2fy. 


EXCHANGE, 

CASE  IV. 

To  reduce  Sterling  to  Flemish  money. 
RULE.     Multiply  the  sterling  by  the  rate  of  exchange, 
dividing  the  product  by  £.1  if  necessary. 

EXAMPLE. 

6.  Remitted  from  London  to  Amsterdam  a  bill  of  £  523 
G  2¥2T  sterling;  to  how  many  pounds  Flemish  kill  it  amount, 
exchange  33  Gd.  Flemish  per  pound  sterling  r 

523  6  2/TX-i02-r-lC080=210370  pcnce^£,C76   10  1CL 

33  C.d.        £.1 
1 2  20 

vn  20 

12 


240 
67 

1680 
1440 

16030  Ans.  £.870  10  10  Fiern. 

V.    f'lL&VCE. 

Paris  and  Bourdcaux  are  the  principal  places  of  exchange 
in  France ;  where  the  business  wf exchange  is  particularly 
studied. 

Accounts  are   kept  throughout  the  French  dominions  in 
Livres,  Sols   and   Denier*,   divided  as  the   British  Pound. 
In  exchange  with   France,  England   pays    so  many   pence 
sterling  for  their  crown,  or  ecu  of  3  livres,,  or  CO  sols  tour- 
nois  =  4  6d.  sterling,  exchange  at  par. 
12  Deniers  =  1   Sol, 
£0  Sols        —  1   Livre. 

3  Livres    =  1   Crown. 
The  Livre  iournois  is  =  to  184  cents  in  the  United  States 

CASE  T. 

To  reduce  Livres  to  Federal  money. 

HVLE.  Multiply  tie  livres  by  18|,  or  rate  of  exchange, 
and  the  product  will  be  cents.  If  sols  are  given  \vitl- 


Hvres,  reduce  ihejn  lo   the  decimal  of  u  li^re ;    multiply  as 
before,  and  the  product  will  be-  mills. 

EXAMPLES. 

t.  Reduce  8440  livres  to  dollars  awl  cent*» 
8440=Iivreg. 

18i=>value  of  1  livre. 

67  520 
8440 
4220=£  cent. 

$1561,40 

Ans.  81561,40. 

2.  My  correspondent  writes  me,  advising  of  the  safe  ar- 
rival oft  he  brig  Huntress  at  Bourdeaux,  and  that  he  had 
received  in  good  condition  lhe_g£ods  shipped  arid  consign? 
»jd  to  him  for  my  account  ;  that  the  net  proceeds,  after  de- 
ducting freight,    duties,  commission,  &e. ;      amounted    lo 
74101  livres  10  sols,  exchange  at  20  cents  per  livre;  with 
what  sum  in  Federal  money  must  I  debit  his  account? 
71101,5  =^Iivres  and  sols. 
20= rate  of  exchange. 


814820,30,0  Ans.  £14820,30. 

CASE  IT. 

To  reduce  Federal  Money  to  Livresf 
.     Divide  the  given1  sum  by    18^  or  llie  rate  of  ex 
ciange,  the  quotient  will  be  ihe answer. 

EXAMPLES. 

3.  Reduce  gl 56 1,40  to  livres. 
18,5)1561,40,0(8440 

Ans.  "8440  livres« 

NOTE.  To  change  French  to  Sterling,  say,  As  one  crown  is 
to  the  given  rate  of  exchange  ;  so  is  the  French  sum  to  the  Sterling 
money  ;  also,  To  change  Sterling  to  French,  say,  As  the  rate  of  ex- 
change, is  to  one  crown,  so  is  the  Sterling  to  the  French  money. 

VI.    SPAIN. 

The  monies  in  Spain  are  of  two  sorts;  the.  one  is  called 
plate  money,  by   which  is  understood,  silver  money;   the 
'her  is  called  vellon. 


EXCHANGE, 

Foreign  bankers  or  remitters  at  Madrid,  Cadiz,  Seville., 
&c.  keep  iheir  accounts  in  piastres,  rials  and  mervadies, 
reckoning  34  mervadies  to  a  rial,  and  3  rials  to  a  piastre, 
the  par  of  which  is  3  Id.  sterling. 

The  shop-keeper  at  Madrid,  the  custom-house,  and  other 
deal  era  wiihiti  the  kingdom  keep  their  accounts  in  rials 
and  mervadies  veilou. 

The  doubloon  of  exchange  is  equal  to  4  piastres  or  32 
mis. 

Accounts  also  are  kept  in  dollars,  rials  and  mervadies.> 
and  exchange  by  the  piece  of  eight  =  4  tid.  at  par. 

34  mervadies  =  1  rial. 

8  rials     .      =  1  piastre  or  piece  of  eight. 
10  rials     .      =  1  dollar. 

The  rial  plate  is  =  10  cents,  and  the  rial  vellon  5  cents 
in  the  United  States;  therefore, 

Jb  reduce  Rials  Plate  and  Rials  Vellon  to  Federal  Money. 

RULE.     Multiply  the  rials  plate  by   10,  aud  the 
vellon  by  5,  the  product  will  be  the  answer. 

EXAMPLES. 

1.  Reduce  8471  rials  plate  to  dollars  and  cents,' 

8474 
10 

$847,40  Ans.  $847,40. 

2.  Reduce  8354  rials  vellon  to  dollars  and  cents. 

8354 


£417,70  Ans.  §417,70. 

London  remits  to  Cadiz  £.874  12  4  sterling,  ex- 
change at  37frf.  per  piastre;  how  much  will  be  received 
for  this  remittance  at  Cadiz  ? 

37|         874  12  4x8-5-303=5542,1254= 
8  5542- piastres  1  rial 

203 

15* 


EXCHANGE. 

'VII.    PORTUGAL. 

Accounts  are  kept  at  Oporto  and  Lisbon  in  reas  and  ex- 
change on  the  milrea=5  7$  sterling,  at  par,  or  $1,25  in  the 
United  States.  1000  reas=l  milrea. 

CAGE  I. 

To  change  Miireas  and  Iteas  io  Federal  Money. 
RULE.     Multiply  the  given  sum  by   1,25   and   cut  off 
three  right  hand  figures  for  decimals  of  a  cent ;  or  add  £ 
to  the  given  sum  and  the  answer  will  be  dollars  and  parts 
of  a  dollar. 

EXAMPLE. 

1.  My  correspondent  at  Oporto  advises  of  the  sales  of 
goods  shipped  and  consigned  to  him,  the  net  proceeds,  af- 
ter deducting  commissions,  duties,  See.  amounted  to  14637 
mil  reas,  800  reas,  exchange  at  &1,25;  how  much  must  he 
!>e  debited  ? 

14637,800  Or     1)14637,800 

1,25  3659450 

73189000  $J 8297,25,0  as  before. 

292756 
146378 


$18297,25,000  Ans.  $18297.25. 

CASE  II. 

To  reduce  Federal  Money  to  Milreas. 
RULE.     Subtract  ^  from  the  federal  money  carrying  the 
division  to  three  places  from  the  dollars,  the  remainder 
be  miireas  and  reas. 

EXAMPLE. 

2.     Reduce  $1 8297,25  to  miireas,  a  &1,25  per  milrea. 
4)18297,25,0 
3659450 


1 4637,800        Aus.  14637  tnilreas,  800  reas. 

VIII.    DENMARK 

Accounts  are  kept  at  Denmark  in  Current  Dollars  and 
Skillings  reckoning  96  skillings  to  the  dollar.  The  rix 
dollar  is=$l  in  the  United  States, 


EXCHANGE. 

To  change  Danish  to  Federal  Money, 
RULE.     The  rix  dollars  being  equal  to  Federal  Dollars, 
therefore  find  the  value  of  the  parts,  aud  annex  it  to  the 
dollars. 

EXAMPLE. 

In  14786  rix  dollars  and  50  skillings  how  many  dollars 
and  cents,  exchange  100  cents  per  rix  dollar  ? 
14786,50 
96 


814786,48,00  Ans.  $14786,48. 

IX.    EAST-INDIA  MONEY. 

1.     BENGAL. 

Accounts  are  kept  at  Madras  in  Pagodas,  Faoams,  and 
Cash. 

80  cash=l  Fanam. 
36  Fanams=l  Pagoda. 
1  Pagoda=Sl,94  in  the  United  States. 

To  change  Pagodas  into  Federal  Money. 
RULE.     Multiply  by  1,94. 

2.    CALCUTTA, 

Accounts  are  kept  in  Rupees,  Annas,  and  Pice* 
12  pice=l  anna. 
16  annas=l  rupee. 
The  rupee  of  Bengal=55|  cents  in  the  United  States; 

To  change  Rupees  to  Federal  Money. 
RULE.     Multiply  by  55|. 

3.    CHINA. 

Accounts  are  kept  in  Tales,  Mace,  Candareens  and  Cash. 
10  cash     ...     =1  candareen. 
10  candareens  .     =1  mace. 

10  mace   .     .     .    =1  tale,  which  is  equal  to  gl,43 

iu  the  United  States. 


CONJOINED  PROPORTION. 

To  change  Tales  to  Federal  Money. 
RULE.     Multiply  tales  by  1,48. 

NOTE.  Those  who  wish  to  acquire  a  more  particular  knowledge, 
of  Foreign  Exchange  may  find  a  very  extensive  and  excellent  treatise 
on,  the  subject,  in  u  Walsh's  Mercantile  Arithmetic." 


CONJOINED  PROPORTION. 

CONJOINED  PROPORTION  is  when  the  coins,  weights  and 
measures  of  several  countries  are  compared  in  the  same 
question,  and  discovers  their  relation,  one  to  another. 

CASE  I. 

When  it  is  required  to  find  how  many  of  the  first  sort  of 

coin,  weight  or  measure,  given  in  the  question, 

are  equal  to  a  given  quantity  of  the  last. 

RULE.  1.  Place  the  numbers  alternately,  beginning  at 
the  left  hand,  and  let  the  last  number  stand  on  the  left 
hand. 

2.  Multiply  the  first  column  continually  for  a  dividend, 
and  the  second  for  a  divisor. 

PROOF.  Make  as  many  statements  in  the  Rule  of  Three 
Direct  as  the  question  requires. 

EXAMPLES. 

1.  If  $4  are  worth  40s.  and  30s.  6   crowns,  and   120 
crowns,  worth  £30,  and  £42  40  guineas,  how  many  dollars 
are  equal  to  1300  guineas  ? 
Left.  Right. 

$4=40*.     Left  4  X  30  X 1 20  X  42  X 1 300=786240000=cli  vidcnd. 
s.  30=6  cro.     Right  40 X6x30x40=288000=di visor. 
cro,  120=30,£ 

£.  42=40  guin.         And  7862400000~:-288000=2730  dolls. 
guin.  1300=$  Ans.  $2730. 

CASE  II. 

When  it  is  required  to  find  how  many  of  the  last  sort  of  coin , 
weight  or  measure,  given  in  the  question,  are 

equal  to  a  quantity  of  the  first. 

RULE.  1.  Place  the  numbers  alternately,  beginning  at 
the  left  hand,  and  let  the  last  given  number  stand  ou  the 
right, 


ARBITRATION  OF  EXCHANGES. 

2.  Multiply  (he  first  column  continually  together  for  a 
divisor,  and  the  second  for  a  dividend. 

EXAMPLE. 

2.  If20lb.  at  Boston  are  equal  to  18lb.  at  Rotterdam ; 
180lb.  at  Rotterdam,  224lb.  at  Versailles;  how  many 
pounds  at  Versailles  are  equal  to  lOOlb.  at  Boston  ? 

Left. 

Boston  20=18  Rotterdam.     Left  20Xl80=3600=divisor. 

Rotterdam  180=224  Versailles.    Right  1 8X224 X  100=403200=div. 
Boston  100.      And  403206-^3600=851 121b.        ABS. 


ARBITRATION  OF  EXCHANGES. 

ARBITRATION  OF  EXCHANGES  means  a  method  of  choos- 
ing the  best  way  oi'  remi'.tiiig  money  abroad,  with  the 
greatest  advantage. 

It  is  by  comparing  the  par  of  Exchange,  already  found, 
with  the  present  course  of  Exchange,  that  the  best  \vay  to 
remit,  or  draw,  to  most  advantage  can  lie  determined/  It 
is  performed  by  Conjoined  Proportion. 

EXAMPLES. 

My  Correspondent  at  Rotterdam  has  §3500,  which  he 
can  remit  by  way  of  Oporto,  at  840  reas  per  dollar,  from 
Oporto  to  Boston  at  8  2d.  per  milrea  (or  1000  reas) ; — Or 
he  can  remit  by  way  of  Roehelle  at  5§  livres  per  dollar, 
and  from  Roehelle  to  Boston  at  6  8d.  per  crown  ;  which 
circular  remittance  is  the  most  advantageous,  and  what  is 
the  difference  ? 
First. 

gl  at  Rotterdam=840  reas  at  Oporto. 
Reas  1000  at  Oporto  ..  =98rf.  at  Boston. 
1000x1=1000  divisor.      $3500  at  Rotterdam. 
840x98x3500=288 1 20000=dividend. 
288120000—1000=288120  pence. 
12288120 


24010  shillings. 

g4001,66-,6f  by  way  of  Oporto. 


INVOLUTION- 

Secondly* 

$1  at  Rotterdam=5|  livres  at  Rochelle, 
Livres6  at  Rochelle=80t/.  at  Boston. 
lX6=6==divisor.     $35 JO  at  Roehelle. 
80x5fx3500=1512000=divideiH}. 
1512000-v-6=25200Q  pence. 
12252000 

6    21000  shillings. 

S3500  by  way  of  Rochelle  ;  consequently  the  rex 
mittance  by  way  of  Cporto  is  most  advantageous,  making 
the  difference  of  §501,66,6f  Ans. 

The  difference  of  the  remittance  wholly  depends  on  the 
Course  of  Exchange  at  the  time;  an  extensive  correspon- 
dence therefore,  is  absolutely  necessary  to  acquire  a 
thorough  knowledge  of  the  Course  of  Exchange  to  make 
this  kind  of  remittance  profitable. 


INVOLUTION. 

INVOLUTION  is  the  finding  of  power.?. 

If  a  number  is  continually  multiplied  by  itself,  the  sev- 
eral products  are  called  "powers"  of  that  number;  thus, 
2  :  4  :  8  :  16  :  32  :  64  :  128  are  powers  of  the  number  2.' 

NOTE.  These  powers  exist  in  nature,  viz.  a  root  is  represented  by 
a  line  or  .<ide  having  only  one  detention,  viz.  length  ;  the  square  is 
a  plain  figure  of  two  dimension?,  viz.  length  and  breadth  !  the  caLc 
has  three  dimensions,  viz.  length,  breadth  and  thickness.  All  the  su- 
perior powers  have  no  existence  in  nature,  but  are  composed  of  a 
multiplication  of  any  number  four  or  more  times  into  itself.  So, 
2X2X  2X2X2=32,*  the  sursolid  or  5th  power,  whose  root  is  2,  has 
no  existence  in  nature,  but  may  be  understood  as  a  series  cf  numbers 
in  geometrical  progression. 

Powers  are  numbered  1st,  2d,  3d,  4lb,&c.  and  sometimes 
are  called  the  square,  cube,  biquadrate,  &e. 

The  figures,  used  to  distinguish  one  power  from  another, 
are  called  indices  and  exponents^  and  are  placed  at  the  top 
on  the  right  hand  ;  thus,  32,  43  ; 


Thus  are  3*  :  $    :  27°:  81*     jimliees?  of  the  number  3. 

<  powers  5 


EVOLUTION-. 


175 


To  raise  a  number  to  any  power. 

RULE.  Multiply  the  given  number  by  itself  continually, 
until  the  number  of  products  is  as  many,  except  one,  as  the 
index  of  the  power  to  be  found. 

1.  What  is  the  square,  or  second  power,  of  21  ? 
21.x21=441=square  of  21.  ^Vns.  441. 

2.  What  is  the  cube  of  4  ? 

4x4x4=64=eube  or  third  power.  Ans.  64. 

3.  What  is  the  biquadrate  or  fourth  power  of  9  ? 
9x9x9x9=6561.  Ans.  6561. 

4.  What  is  the  fourth  power  of  1,05  ? 

Ans.  1,21550625. 

To  raise  Vulgar  Fractions  to  any  power. 
RULE.     Raise  both  of  the  terms  of  the  fraction  to  the 
power  required,  as  before  directed. 

If  a  mixt  number  is  proposed,  either  reduce  it  to  an  im- 
proper fraction  and  work  as  before,  or  reduce  the  vulgar 
fraction  to  a  decimal,  and  proceed  as  in  the  whole  numbers. 
EXAMPLES. 

5.  Raise  f  to  the  fourth  power. 

Numer.  5x5x5x5  =  625 


Denom.  8x8x8x8=4096  Ans. 

6.  What  is  the  square  of  4|  ?    Ans.  V/  or  19,36  decimal. 

NOTE.  In  a  series  of  powers,  the  sum  of  any  two  indices  is  the 
index  of  a  power,  which  is  the  product  of  the  two  powers  whose  in- 
dices were  added.  And  the  difference  of  any  two  indices  is  the  in- 
dex of  a  power,  which  is  the  quotient  of  the  two  powers  whose  indi- 
ces were  subtracted.  Hence  any  power,  above  the  third,  may  be 
easily  found  without  producing  all  the  lower  powers. 

Thus  to  find  the  7th  power  of  any  number,  because  4  and  3  make 
7,  multiply  the  4th  power,  by  the  3d,  the  product  will  be  the  7th 
.power.  Again,  multiply  the  7th  power  by  the  5th  the  product  will 
be  the  12th  power,  because  7  and  5  added  are  equal  to  12,  and  so 
for  any  other, 


EVOLUTION. 

EVOLUTION  is  the  finding  of  the  root  of  any  number. 

The  index  of  the  root,  like  that  of  the  power  in  Involution,  is  one 
more  than  the  number  -of  multiplications,  necessary  to  produce  ^te 
power,  or  given  numbef. 


ffQ  SQUARE  ROOT, 

NOTE  1.  Roots  are  sometimes  denoted  by  this  character  tj  be- 
Jbre  the  power  with  the  index  of  the  root  against  it;  thus,  ^/3  64 
signifies  the  third  root  or  cube  of  64. 

2.  There  will  always  be  as  many  figures  in  the  root  as  there  are 
periods  in  the  given  power. 

To  extract  the  square  root  is  to  find  out  such  a  number,  as, 
being  multiplied  into  itself,  will  produce  the  given  number, 


SQUARE  HOOT. 

GENERAL  RULE. 

1  Point  the  given  number,  beginning  at  the  right  hand, 
into  periods  of  two  figures  each. 

2.  Find  the  greatest  square  in  the  first  or  left  hand  pe- 
riod, and  place  it  under  this   period,   and  its  root   in   the 
quotient  ;  subtract  the  square  number  from  the  first  period, 
and  to  the    remainder  bring  down  the   next    period  and[ 
call  this  the  Resolvend. 

3.  Double  the  quotient  for  a  divisor. 

4.  Find  ho\v  often  the  divisor  is  contained  in  the  Resol- 
vend, omitting  the  unit  figure,  and  place  the  answer  in  the 
quotient  and  at  the  right  hand  of  the  divisor. 

5.  Multiply  this  divisor  by  the  last  quotient  figure  and 
subtract  the  product  fr«m  the  Resolvend  ;  to  the  remainder 
bring  down  the  next  period,  and  proceed  as  before,  till  all 
the  periods  are  brought  down  5  the  figures  in  the  quotient 
•will  be  the  root. 

PROOF.  Multiply  the  quotient,  or  root,  by  itself,  adding 
the  remainder,  if  any,  the  sum  will  be  equal  to  the  given, 
number  or  power.  This  method  of  proof  will  apply  to  the 
roots  of  any  power. 

EXAMPLES. 
What  is  the  square  root  of  1522756  ? 

i  522756  (1234=rsquare  root 
Divisors  1 

Double  the  quot.=22)52=resolvend. 
44 

Double  the  quot.=243)827=resolvend. 

729 

Double  the  quot.=2464)9856=resolvend. 
9&56 

0"  Ans.  1234. 


SQUARE  HOOT. 

2.  What  is  the  square  root  of  83521  ?  Ans  289. 

3.  What  is  the  square  root  of  5499025  ?     Ans.  2345. 

NOTE.  If,  after  all  the  periods  are  used,  there  is  a  remainder,  the 
given  number  is  not  a  square  number,  and  therefore  has  no  exact  in- 
tegral root ;  but  it  is  a  surd,  that  is,  a  number  whose  root  can  never 
be  exactly  found,  but  may  be  approximated  by  annexing  ciphers  con- 
tinually to  the  remainder  in  periods  of  two  each,  and  the  quotient 
will  be  the  answer,  giving  as  many  whole  numbers  in  the  root  as 
there  are  periods  of  whole  numbers,  and  as  many  decimals  as  there 
are  periods  of  decimals. 

EXAMPLE. 

4.  What  is  the  scfuare  root  of  7  ? 

7,000000  divided  by  the  general  rule  =   Ans.  2,6  45f. 

NOTE,  When  the  given  number  consists  of  a  whole  number  and 
decimals  together,  make  the  number  of  decimals  even  by  annexing 
ciphers  to  them,  so  that  a  point  may  fall  on  the  unit's  place  of  the 
whole  number,  and  proceed  as  directed  in  the  General  Rule. 

EXAMPLES. 

5.  What  is  the  square  root  of  234,723  ? 

234,7230  which  divided  by  the  general  rule  will  give 

15,32f  Ans. 

6.  What  is  the  square  root  of  ,00032754  ? 

Ans.  ,018091. 

To  extract  the  Square  Root  of  a  Vulgar  Fraction. 

RULE.     1.  Reduce  the  fraction  to  its  lowest  terms. 

2.  Extract  the  square  root  of  the  numerator  for  a  new 
numerator,  and  the  square  root  of  the  denominator  for  anew 
denominator.  But  if  the  fraction  is  a  surd,  that  is,  a  num- 
ber whose  root  cannot  be  exactly  found,  rednce  it  to  a  deci- 
mal and  extract  its  root  as  directed  in  the  general  rule. 

EXAMPLES. 

7.  What  is  the  square  root  of  f  ? 

¥=f  •  Ans.  f . 

8.  What  is  the  square  root  of  yV^VV  •  Ans.  |. 

9.  What  is  the  square  root  of  tfae  §ard  £|f  ? 

K-=,«064516129t.    V%8&4616i294s9802t  Ans. 
16 


178  ^UBE  ROOT. 

To  extract  the  Square  Root  of  a  mixed  number. 

RULE.  1.  Reduce  the  fractional  part  to  its  lowest 
terms,  and  the  mixt  number  to  an  improper  fraction. 

2.  Extract  the  root  of  the  numerator  and  denominator 
for  a  new  numerator  and  denominator. 

If  the  mixt  number  is  a  surd,  reduce  the  fractional  part 
to  a  decimal,  annex  it  to  the  whole  number,  and  extract  its 
square  root. 

EXAMPLES. 

10.  What  is  the  square  root  of  51|i  ? 


51fi=1|f  «  and  y^ff  6=3j»=7i.  Ans.  7|. 

11.  What  is  the  square  root  of  27T%  ?  Ans.  5£. 

12.  What  is  the  square  root  of  the  surd  6§  ? 

6|=6j666666f.     And  ^/6,666666=2,581f. 

Ans.  2,58  If. 

13.  A  general  has  an  army  composed  of  103041  men, 
and  wishes  to  form  them  into  a  square;   how  many  must 
be  placed  in  rank  and  file  ?  Ans.  321. 


CUBE  ROOT. 

To  extract  the  Cube  Root  of  any  number. 
RULE.     1.  Point  the  given   number,  beginning  at  the 
right  hand,  into  periods  of  three  figures  each. 

2.  Find  the  greatest  cube  of  the  first  period   and  sub- 
tract  it  from  the  first  period ;  put  this  root  in  the  quotient, 
and  to  the  remainder  bring  down  the  next  period  and  call 
it  the  resolyend. 

3.  Square   the    quotient  and    multiply   it  by   3  for  a 
divisor. 

4.  Find  how  often  the  divisor  is  contained  in   the  resol- 
vend,  rejecting  the  units  and  tens,  and  put  the  answer  in  the 
quotient. 

5.  Square  the  last  figure  in  the  quotient,  and  place  it  on 
the  right  hand  of  the  divisor,   always  putting  a  cipher  in 
the  place  of  tens,  when  the  quotient  figure  is  less  than 
four. 

6.  Multiply  the  last  figure  in  the  quotient  by  3  and  its 
product  by  the  preceding  figure  in  the  quotient  5  place  it 


CUBE  ROOT. 

under  the  last  divisor,  putting  units  under  tens  ;  add  them 
together  and  multiply  their  sum  by  the  last  quotient  figure 
for  the  subtrahend,  which  subtract  from  the  resolvend, 
bring  down  the  next  period,  and  proceed  as  before. 

EXAMPLES. 

1.  What  is  the  cube  root  of  1860867? 

Square  of  1x3  =  3=divisor.  1860867(123 

Square  of  2  put  to  3=304  1 

2X3X1=         6  

860  =  resolvena 

"364x2=subtrahend.728 

132367=resol. 

Square  of  12x3=432=  divisor. 
Square  of  3  put  to  43209 
3x3x12  =  108 

44289x3=subtrahend    1S2867 

0 

2.  What  is  the  cube  root  of  94818816  ?         Ans.  456. 

3.  What  is  the  cube  root  of  3826571 76  ?        Ans.  726, 

4.  What  is  the  cube  root  of  12812904  ?         Ans.  234. 

To  extract  the  Cube  Root  of  a  Vulgar  Fraction. 

RULE.  1.  Reduce  the  fraction  to  its  lowest  terms,  and 
extract  the  cube  root  of  its  numerator  and  denominator. 
If  the  fraction  is  a  surd,  reduce  it  to  a  decimal  and  extract 
its  root. 

NOTE.  In  pointing  for  decimals,  begin  at  the  left  hand  and  make 
the  first  three  figures,  next  to  the  decimal  point,  the  first  period  ;  and 
it'  the  period  on  the  left  is  not  complete,  make  it  up  with  ciphers, 
Tliis  must  be  observed  both  in  pure  fractions  and  mixt  numbers. 

EXAMPLES. 

5.  What  is  the  cube  root  of  fVW  ?  Ans.  f . 

6.  What  is  the  cube  root  of  H?  Ans.  1.1447. 
7-  What  is  the  cube  root  of  the  surd  f  ?  Ans.  873f. 

To  extract  the  Biquadrate  Root. 

RULE.  Find  the  square  root  of  the  given  number,  anrf 
extract  the  square  of  that  square  root. 


18Q  CUBE  ROOT. 

EXAMPLES. 

1.  What  is  the  biquadrate  root  of  228886641  ? 

Ans.  123. 

2.  What  is  the  biquadrate  root  of  43237380096  ? 

Ans.  456- 

NOTE.  Although  the  rules  may  be  given  for  reducing  the  roots  of 
higher  powers,  they  are  scarcely  worth  the  pupil's  labor,  as  their 
operations  are  very  tedious,  and  seldom  necessary  ;  and  when  they 
do  occur,  the  work  may  be  easily  performed  by  logarithms, 

To  extract  Roots  by  Logarithms. 

RULE.  Divide  the  given  number  by  the  index  of  the 
given- power,  whose  root  is  to  be  extracted,  the  quotient 
will  be  the  logarithm  of  the  root ;  that  is,  divide  by  2  for  the 
square  root  ;  3  for  (he  cube;  4  for  the  biquadrate 5  5  for 
the  sursolid  or  fifth  power,  &e. 

EXAMPLE. 

1.  What  is  the  sursolid  or  5  power  of  31,25  ? 
The  logarithm  of  31,25  =  1.4948500 

One  fifth,  is  the  logarithm  of  the  root  1,990,  &e. 

=0,2989700  Ans. 
General  Rule  for  extracting  Roots  of  all  powers. 

HULK.  1.  Prepare  the  given  number  for  extraction,  as 
the  root  requires. 

2.  Find  the   first   figure  in  the  root,   and    subtract  its 
power  from  the  given  number,  and  to  the  remainder  bring 
clown  the  first  figure  of  the  next  period  and  call  it  the  divi- 
dend. 

3.  Involve  the  root  already  found  to  the  power  next  infe- 
rior to  that  which  is  given,  and  multiply  it  by  the  number 
denoting  the  given  power  for  a  divisor. 

4.  Find  how  often  the  divisor  may  be   had  in  the   divi- 
dend,  and  the  quotient  will  be  another  figure  of  the  root. 

5.  Involve  the  whole  root  to  the  given  power,  and  sub- 
tract it  from  the  given  number,  as  before. 

6.  Bring  down  the  first  figure  of  the  next  period  to  the 
remainder  for  a  dividend,  to  which  find  smew  divisor,  and 
ao  continue  till  the  whole  is  finished. 

EXAMPLES. 

1.  What  is  the  cube  root  of  30959144  ?         Ans.  314. 

2.  What  is  the  biquadrate  root  of  3664966416  ? 

Ans.  202. 


ARITHMETICAL  PROGRESSION, 


ARITHMETICAL  PROGRESSION. 

ARITHMETICAL  PROGRESSION  is  a  series  of  numbers  in- 
creasing or  decreasing  by  a  common  difference,  or  by  a  con- 
tinual addition  or  subtraction  of  some  equal  numbers. 

There  are  five  things  in  Arithmetical  Progression,  any 
three  of  which  being  given,  the  other  two  may  be  found. 


3.  The  number  of  terms. 

4.  The  common  difference. 

5.  The  sum  of  all  the  terms, 

NOTE.  1.  If  any  three  numbers  are  in  Arithmetical  Progression, 
the  sum  of  the  two  extremes  will  be  equal  to  double  the  mean  or 
Kiddle  number ;  thus,  4 . 9  .  14  .  that  is,  4+14=18=9x2=18. 

2.  If  four  numbers  are  in  Arithmetical  Progression,  the  sum  of  the 
two  extremes  will  be  equal  to  the  sum  of  the  two  means  or  middle 
numbers  ;  thus,  2.5.3.11.  that  is,  2+11=13=5+8=13. 

3.  If  many  numbers  are  in  Arithmetical  Progression,  the  sum  of  the 
two  extremes  will  be  equal  to  the  sum  of  any  two  means  that  arc 
equally  distant  from  the  extremes  ;  -thus, 

5  .  8  .  11  .  14  .  17  .  20;  5+20=25=8+17=25=11+14=25. 

4.  If  the  numbers  are  odd,  the  sum  of  the  two  extremes  will  be 
equal  to  the  sum  of  any  two  means  equally  distant   from  them,  and 
all  be  equal  to  double  the  odd  mean  or  middle  number  ;  thus,  3  .  7  ., 
11   .  15  .  19  .  23.  27  ^  3+27=30=7+23=30=11+19=30=15 


PROPORTION  I. 

The  two  extremes  and  number  of  terms  being  given,  to  find' 
the  common  difference. 

RULE.  Subtract  the  less  from  the  greater  extreme,  and 
divide  the  remainder  by  the  number  of  terms,  less  one,  the 
quotient  will  be  the  common  difference. 

EXAMPLES, 

1.  What  is  the  common  difference  of  11  terms  of  as 
arithmetical  series,  whose  extremes  are  3  and  33? 

33—3=30-7-1 1—1  =3  com.  diff.  Ans.  3, 

2.  There  are  8  children  that  differ  alike  in  (heir 

16* 


ARITHMETICAL  PROGRESSION, 


— 2=21-f-0— 1=3  com.  diff.  of  their  ages, 
ngest  2")  4th  .  .  14") 

...51  ,,          3d    .  .  17  I  ,, 

3±  years  old.         gd    ^      2Q  |>  years  old. 

.  .     11 J  Eldest   23  J 


tSio  youngest  is  2  years  old,  and  the  eldest  23  ;  what  is   the 
difference  of  their  ages,  and  the  age  of  each  ? 

23—2=21—8—1=3  com.  diff.  of  their  ages, 
Youngest  2")  4th 

7(h 
6th 
5th 

PROPORTION  II. 
The  two  extremes  and  the  number  of  terms  being  given,  to 

find  the  sum  of  all  the  terms. 

RULE.  Multiply  the  sum  of  the  two  extremes  hy  half 
'he  number  of  terms,  the  product  will  be  the  sum  of  all  the 
terms. 

EXAMPLES. 

3.  What  is   the  sum   of  an    Arithmetical  Progression, 
whose  extremes  are  3  and  33,  and  number  of  terms  11  ? 

3-|-33=36x51=l  98=sum  of  all  the  series.      Ans.  198. 

4.  How  many  times  does  a  clock  strike  in  12  hours  ? 

12-{-l=13x6=78.  Ans.  78, 

PROPOSITION  III. 
The  two  extremes  and  common  difference  being  given,  to 

find  the  number  of  terms. 

RULE.  Subtract  the  less  from  the  greater  extreme,  and 
divide  the  remainder  by  the  common  difference,  the  quo- 
tient plus  one  will  be  the  number  of  terms. 

EXAMPLES. 

'j.  The  two  extremes  are  3  and  33,  and  the  common  dif- 
ference 3  ;  what  is  tlie  number  of  terms  ? 

33 — 3=30-r-3=10-j-l=ll=number  of  terms  Ans. 
6.  A  man  starting  from  Boston  to  travel   to  a  certain 
place,  his  first  day's  journey  was  G  miles,  and  his  last  was 
40  miles ;  he  increased  his   travelling  each  day  4  miles , 
how  many  days  did  he  travel  ? 

40 — 6=34-f-4= 8, i-f-1  =9  i.  Ans.  9 A  days. 

PROPOSITION  IV. 
Either  of  the  extremes,  the  number  of  terms,  and  common 

difference  being  given,  to  find  the  other  extreme. 
RULE.  Multiply  the  common  difference  into  the  num- 
ber ef  terms  minus  one,  subtract  the  product  from  the 
greater  extreme,  the  remainder  will  be  the  less  extreme;  or 
add  the  less  extreme  to  that  product  the  sum  will  be  the 
greater  extreme. 


GEOMETRICAL  PROGRESSION, 
EXAMPLES. 

7.  The  less  extreme  is  3,  the  greater  33,  the  number  of 
terms  11,  and  the  common  difference  3;  either  extreme  is 
required.     3x10=30 — 33=3  less  extreme.     And  3x10= 
30+3 =33= greater  extreme.  Ans.  3  and  33. 

8.  A  man  in  7  days  travelled  from  Boston  to  New-York, 
he  increased  each  day's  journey  by  3  miles,  his  last  day's 
journey  was  45  miles ;   what  was  the  first  day's  journey, 
and  how  many  miles  did  h»  travel  ? 

Number  of  terras  7— 1=6x3=18— 45=27=  1st  days  jour'y. 
By  proposition  II.     27+45=72x3i=252=number  miles, 

C  27  miles. 

?  Distance  252  miles. 


GEOMETRICAL  PROGRESSION 

GEOMETRICAL  PROGRESSION  is  when  any  series  of  nnm- 
bers  increase  by  one  common  multiplier,  or  decrease  by  one 
common  divisor;  as,  2  :  4  :  8  :  16  :  32  ;  here  2  is  the 
common  multiplier.  And  64  :  32  :  16  :  8  :  4  :  2  5 
here  2  is  the  common  divisor. 

NOTE.     The  common  multiplier,  or  divisor,  is  called  the  ratio. 

In  any  Geometrical  Progression  the  same  things  are  to  be  observed 
as  in  Arithmetical  Progression,  viz. 

1.  The  extremes,  or  first  and  last  terms. 

2.  The  number  of  terms. 

3.  The  ratio,  or  common  multiplier  or  divisor. 

4.  The  sum  of  all  the  series  ;  any  three  of  which  being  known,  the 
others  may  be  found. 

NOTE.  1.  If  any  three  numbers  are  in  Geometrical  Prog-re?:- ion., 
the  product  of  the  two  extremes  will  be  equal  to  the  square  of  the 
mean  or  middle  number,  thus,  4  .  8  .  16  ;  4X16=64=8X8=64. 

2.  If  four  numbers  are  in  Geometrical  Progression,  the  product  of 
the  two  extremes  will  be   equal  to  the  product  of  the  two  means  ov 
middle  numbers  j  thus,  81  .  27  .  9  .  3  ;  81X3=243=27X9=243, 

3.  If  many  numbers  are  in  Geometrical  Progression,  the  product  of 
the  two  extremes  will  be  equal  to  the  product  of  any  two  means  that 
are  equally  distant  from  them  ;  thus,  2.4.8.   16  .  32  .  64  ;  2X 
64=1 28=4X32==  125=8  X  16=128. 

4.  If  the  numbers  are  odd.  the  product  of  any  two  extremes  will  be 
equal  to  the  square  of  the  mean;    thus,  2  .  4  .  8  >  16  -  32  j  2X 
32=64=4  X  16=64=8  X8=64, 


GEOMETRICAL  PROGRESSION, 

PROPOSITION  I. 
The  two  extremes  and  common  ratio  being  given,  to  find  the 

sum  of  all  the  series. 

RULE.  Multiply  the  greater  extreme  by  the  common 
ratio,  subtract  the  less  extreme  from  the  product,  and  di- 
vide the  remainder  by  the  common  ratio  minus  one,  the 
quotient  will  be  the  series. 

EXAMPLES. 

1.  What  is  the  sum  of  a  geometrical  series,  whose  ex- 
tremes afe  2  and  4374  and  the  common  ratio  3  ? 

4374x3=13122—2=13120—3—1=6560  Ans. 

2.  A  gentleman  marrying,  received  from  his  father-in- 
law  one  dollar,  on  condition,  that  he  was  to  receive  a  pre- 
sent on  the  first  day  of  every  month  for  the  first  year,  which 
should  be  double  still  to  what  he  had  the  month  before  5 
what  was  the  lady's  fortune  ?  Aiis.  ^095. 

PROPOSITION  II. 

The  less  extreme,  common  ratio,  and  number  of  terms  being 

given,  to  find  the  greater  extreme. 

RULE,  Raise  the  ratio  to  a  power  denoted  by  the  num- 
ber of  terms  minus  one,  and  multiply  that  power  by  the 
less  extreme,  the  product  will  be  the  greater  extreme. 

EXAMPLES. 

3.  The  less  extreme  is  4,  the  common  ratio  2,  and  num- 
ber of  terms  10;  what  is  the  greater  extreme  ? 

29x4=2048=greater  extreme.  Ans.  2048. 

4.  What  debt  will  be  discharged  in  12  months  by  pay- 
ing gl  the  first  monih,   §2  the  second,  each  month  paying 
double  to  the  preceding  payment,  and  what  will  be  the  last 
payment  ?         21 1  —2048X2 — 1=2048  last  payment. 

By  propo.  I.  2048x2=4096—  l  =  $4095=the  debt. 

PROPOSITION  III. 

The  greater  extreme.,  common  ratio,  and  number  of  terms 

being  given,  to  find  the  less  extreme. 
RULE.     Raise  the  ratio  to  a  power  denoted  by  the  num- 
ber of  terms  minus  one,  and  divide  the  greater  extreme  t>j 
that  power,  the  quotient  will  be  the  less  extreme* 


GEOMETRICAL  PROGRESSION. 

EXAMPLE. 

5.  The  greater  extreme  is  2048,   the  common  ratio  2, 
and  the  number  of  terms  10  ;  what  is  the  less  extreme  ? 

29  =  512—2048=4  less  extreme.  Aus.  4. 

PROPOSITION  IV. 

The  two  extremes  and  common  ratio  being  given,  to  find  the 

number  of  terms, 

RULE.  Divide  the  greater  extreme  by  the  less,  and 
raise  the  ratio  to  a  power  equal  to  the  quotient,  add  one  to 
the  index  of  that  power,  and  the  sum  will  be  the  number  of 
terms. 

EXAMPLES. 

6.  The  two  extremes  are  4  and  2048,    the  common  ra- 
tio 2  ;  what  is  the  number  of  terms  ? 

2048-7-4=512.  29=512.     Therefore  9-f  1  =  10  Ana. 

7.  In  what  time   will  a  debt  be  discharged  by  monthly 
payments,  the  first  of  which  is  $1  and  the  last  $2048,  the 
ratio  being  2  ? 

2048-r-l=2048  .  2^=2048.  Therefore  11+1  =  12  ino.  An. 

PROPOSITION  V. 

The  two  extremes  and  number  of  terms  being  given,  to  find 
the  common  ratio. 

RULE.  Divide  the  greater  by  the  less  extreme,  and  ex- 
tract that  root  of  the  quotient,  whose  index  is  denoted  by 
the  number  of  terms  minus  one,  the  root  will  be  the  com- 
mon ratio. 

EXAMPLES. 

8.  The  two  extremes  are  4  and  2048,  and  the  number  of 
terms  10  ;  what  is  the  common  ratio  ? 

2048-r-4=512.     Therefore  5129=2  com.  ratio. 
Or  5123(83=2  com.  ratio  Ans. 

9.  What  will  be  the  ratio  of  the  scries  in  discharging  a 
debt  in  a  year  by  monthly  payments,  the  first  payment  of 
which  is  $1  and  the  last  8204*8  ? 

2048-r-l=2018.     Therefore  204*1* *  —2  common  ratio. 


POSITION, 


POSITION. 

NEGATIVE  ARITHMETIC,  called  the  Rule  of  False,  is 
that,  by  which  a  true  number  is  found  out  by  supposed  num> 
bers. 

Position  is  either  Single  or  Doable. 

SINGLE  POSITION. 

RULE.  Suppose  any  number  at  pleasure,  and  work  it 
according  to  the  nainre  of  the  creation.  If  the  result  fully 
agrees  with  the  conditions  of  the  question,  the  work  i*s 
dene,  and  the  number  supposed  will  be  the  answer  ;  but  if 
not,  proceed  thus, 

As  the  result  of  the  supposition, 
Is  to  the  number  supposed  ; 
So  is  the  given  number  in  the  question, 
To  the  true  number,  or  answer. 
EXAMPLES. 

1.  A  gentleman  had  a  certain  number  of  dollars  in  his 
purse,  the  sum  of  the  third,  fourth  and  sixth  part  of  them 
made  54  ;  how  many  were  in  the  purse  ? 

60=supposed  number.        Then,  as  45  :  60  :  :  54- 
—  54 

20=i  Of  the  supposed  numb. 


=£  ditto.  Proof  3 

10=i  ditto. 
— 
45=rsu m  of  supposition 


72  240 

300 

24  

18         45)3240(72  dolls. 
12 


54  Ans.  872. 

2.  Three  persons  conversing  about  their  ages,  said  the 
first,  I  am  so  old ;  said  the  second,  I  am  as  old  again  as 
that ;  and  said  the  third,  I  am  as  old  as  the  first  and  half 
as  old  as  the  second  ;  their  ages  taken  together  make  108 
vears  $  what  is  the  age  of  each? 

("First      21|. 
Ans.«  Second  434. 
(.Third    431. 
DOUBLE  POSITION. 

DOUBLE  POSITION  requires  two  suppositions,  which 
must  be  used  ai-eor^ing  to  the  nature  of  the  question.  If 
either  of  the  supposition*  answer  the  question,  the  work  is 
flone,  but  if  not,  observe  the  following  rule.. 


POSITION. 


187 


RULE..  Compare  the  conditions  of  the  question,  with 
the  results  of  the  suppositions,  and  find  whether  each  sup- 
position is  greater  or  less  than  the  true  answer;  if  greater 
mark  the  excess  with  +•  if  less,  with  — ,  and  set  down 
both  suppositiens  and  their  errors  with  the  signs  opposite 
to  them  ;  then  say, 

As  the  difference  of  the  errors,  if  alike,  or  sum,  if  unlike? 

Is  to  the  difference  of  the  suppositions  5    . 

So  is  either  error, 

To  a  fourth  number ; 

which,  being  added  to  or  subtracted  (as  the  case  may  re- 
quire) from  the  supposition,  opposite  to  the  error  which  is 
used,  will  be  the  true  answer. 

EXAMPLES. 

1.  A  person,  being  asked  the  age  of  each  of  his  sons,  re- 
plied,  that    his   eldest    son   was  4  years   older  than  the 
second;  his  second  4  years  older  than  the  third;    his  third 
son  4  years  older  than  the  fourth,  or  youngest ;    and  his 
youngest  son  was  half  the  age  of  the  oldest ;  what  was  the 
age  of  each  of  his  sons  ? 

First.  sup.  error, 

Suppose  the  youngest  8  years  then  would  the  ages  of        8 2 

the  other  three  be  12,  16,  and  20.  18  -f  3 

Half  of  20=10  and  10 — 8=2=the  first  error,  and  less. • 

10        5 
Secondly. 

Suppose  the  youngest  18  years,  then  would  the  other 
three  be  22,  26  and  30. 

Half  of  30=15  and  18 — 15=3  second  error,  and  more. 
As  5  :  10  :  :  2  :  4-f8=12. 

Or  5  :  10  :  :  3  :  6 — 18=12=the  age  of  the  youngest,  and  the 
ages  of  the  other  three  are  16,  20,  24,  Ans. 

2.  A  boy,  stealing  apples,  was  taken  by  the  owner,  and, 
to  appease  his  anger,  gave  him  half  of  what  he  had,  and 
the  owner  gave  him  back  10  ;  going  a  little  further,  he  met 
a  man  and  was  compelled  to  give  him  half  of  what  he  had 
left,  who  returned  him  back  4;  going  further  he  met   an- 
other person  at  whom  he  gave  half  of  what  he  then  had,  and 
who  gave  him   hack  1  ;   at  length  getting  safe  away,  he 
found,  that  he  had  13  left;  how  many  had  heat  first  ? 

Ans.  60. 


ALLIGATION. 


ALLIGATION. 

BY  the  rule  of  Alligation,  questions,  relating  to  the 
mixing  of  different  simples,  are  resolved,  it  is  either  Me- 
dial or  Alternate. 

ALLIGATION  MEDIAL 

Is  when  there  are  given  the  quantities  and  prices  of  the 
several  simples  to  be  inixt,  to  find  the  price  of  some  quan- 
tity of  the  mixture. 

RULE.     Find  the  values  of  all  the  given  quantities  of 
the  simples  to  be  mixt,  at  the  given  prices,  and  then  say, 
As  the  sum  of  the  quantities  to  be  mixt, 
Is  to  the  sum  of  their  values  ; 

So  is  thatparf,  or  quantity  of  the  mixture  whose  price 
is  sought,     To  its  value. 

EXAMPLE. 

A  grocer,  wishing  to  mix  currants,  takes  18lb.  at  5  cents, 
30lb.  a  6  cents,  and  12lb.  a  8  cents  per  Ib.  5    what  is  the 
value  of  lib.  of  the  mixture  ? 
181b.  a  5c.=  90 
30    .  .  6c,=180 
12    .  .  8e.=  96 

60Ib.     .      183,66 

Ib.        $  Ib. 

As  60  :  3,66  :  :  1  :  6,1m.  Ans, 

ALLIGATION  ALTERNATE. 

Alligation  Alternate  admits  of  several  cases,  but  it  is  of 
very  little  use  in  business. 

RULE.  Take  the  difference  between  each  price,  and 
the  mean  rate,  and  set  them  alternately,  they  will  be  the 
answer;  which  will  be  as  various  as  the  different  modes  of 
linking  them  together. 

EXAMPLE. 

How  much  tea  a  16s.  14s.  9s.  and  8s.  per  Ib.  will  com- 
pose a  mixture  worth  10s.  per  Ib.  ? 
8  -  .  6  a    8s. 


2  «  16s. 
Ans.  4lb-  a  8s.  6  a  9s.  2  a  14s.  and  lib.  a  16s 


PERMUTATION. 


PERMUTATION  AND  COMBINATION  OF  NUM- 
BERS. 

BY  the  Combination  of  numbers  is  meant  the  different 
orders,  into  which  any  number  of  things  can  be  disposed, 
cither  by  Permutations,  Elections,  or  Compositions. 

CASE  I. 

To  find  the  number  of  changes  any  number  of  things  can 

undergo. 

RULE.  Assume  the  natural  series  of  numbers,  1,2,  3, 
&c.  up  to  the  given  number  of  things,  and  multiply  them 
continually  into  one  another,  the  Jast  product  will  be  the 
answer. 

EXAMPLE. 

How  many  changes  can  the  three  first  letters  of  the 
alphabet  undergo  ? 

1X2x3=6  Ans.         Proof.     1.  a  b  c.        4.  b  c  a. 

2    a  c  b.         5.  c  b  a. 
3.  b  a  c.        6.  c  a  b. 

CASE  II. 
To  find  the  number  of  Elections  of  a  less  number  of  things 

from  a  greater  number. 

RULE.  Take  the  natural  order  of  series  1,  2,  3,  &c.  up 
to  the  number  to  be  elected,  and  multiply  them  continually 
together;  then  take  a  series  of  as  many  terms,  decreasing 
by  otie,  down  from  the  number  out  of  which  the  elections 
are  to  be  made,  and  multiply  the  terms  of  it  continually 
together;  divide  the  latter  product  by  the  former,  the 
quotient  will  be  the  answer. 

EXAMPLE. 

How  many  choices  of  2  are  there  in  six  different  things  ? 
Suppose  a  b  c  d  e  f  ,  the  things  proposed, 

1X2=  2.         30^-2-15  Ans     f  ab>  ac'  ad'  ae»  afj==5 
6X5=30.  3  Ans'    I  be,  bd,  be,  bf,=4 

The  elections  are  <{  cd,  ce,  cf,=3 

de,  d£=2 


15 
17 


1 90  PERMUTATION. 

CASE  III. 

To  find  the  number  of  Compositions  of  any  number  of  thing* 
in  an  equal  number  of  sets,  the  things  being  all  different* 

RULE.  Multiply  the  things  in  every  set  into  one  an- 
other continually,  the  product  will  be  the  answer. 

EXAMPLE. 

Suppose  4  companies,  each  consisting  of  10  men,  how- 
many  compositions  of  10  men  each  can  be  drawn  out  from 
them. 

10X10X10X10=10000.  Ans.  10000. 

Application  of  the  preceding  cases. 

1.  Five  travellers  came  to  a   public  house,  and  agreed 
with  the  landlord  to  stay  with  him,  as  long  as  they   with 
him  could  sit  in  a  different  position  every  day  at   dinner; 
how  long  must  they  stay  to  fulfil  the  agreement  ? 

Ans.  720  days. 

2.  A  butcher,  wishing  to  buy  some  sheep,  asked  I  he 
owner  how  much  he  must  give  him  for  20 ;  on  hearing  his 
price,  he  said  it  was  too  much  ;  the  owner  replied,  that  he 
should  have  20,  provided  he  tvvould  give  him  a  cent  for 
each  different  choice  of  10  in  20,  to  which  he  agreed  ;  how 
much  did  he  pay  for  the  10  sheep,  according  to   the   bar- 
gain ?  Ans.  $1347,56. 

3.  How  many  changes  are  there  in  throwing  6  dice  ? 

Ans   4665G. 

4.  How  many  changes  can  be  rung  on  the  8  bells  belong- 
ing to  Christ  Church  in  Boston,  and  how  long  will  all  the 
changes  take  in  ringing  once  over,  allowing  8  changes  to  be 
rung  in  a  minute.  *    »         5  40320  changes, 

'  ?  3  days,  11  hours. 

5.  Two  gamesters  one  day,  at  dice  they  would  play, 
And  being  full  merry  in  wine, 
Says  B.  unto  A.  what  odds  will  you  lay, 
I  cast  not  all  the  six  faces  this  time  ? 
Says  A.  then  to  B.  ten  to  one  I'll  lay  thee, 
With  six  dice  the  six  faces  you  cast  not. 
Pray,  gentlemen,  shew,  and  soon  let  them  know, 
For  the  odds  on  the  cast,  Sirs,  they  know  not. 

Ans.  A.'s  chance  to  that  of  B,  is  as  45936  to  720®,* 
orasG/33to  1. 


SIMPLE  INTEREST  BY  DECIMALS. 


SIMPLE  INTEREST  BY  DECIMALS. 

NOTE.     1.  Let  P  =  the  Principal,  or  sum  put  to  interest. 
R  =  the  Ratio,  or  rate  per  cent. 
T=  the  Time. 
A  =  the  Amount. 
I   =  the  Interest. 

2.  The  ratio  is  the  simple  interest  of  $1  or  £.1  for  one  year  at  the 
rate  per  cent,  proposed,  and  is  thus  found  ; 

ratios. 

As  100  :  4  :  :  1  :  ,04  =  rate  at  4  per  cent. 
100  :  4,5  :  :  1  :  ,045  =  .  .  4£  per  cent. 
100  :  6  :  :  1  :  ,06  =  .  .6  per  cent. 

3.  All  the  various  cases  which  can  possibly  take  place   in  Simple 
Interest,  may  be  expressed  by  five  theorems,  which  will  be  annexed 
to  each  case. 

4.  When  two  or  more  letters  are  joined  together  like  a  word,  they 
are  to  be  multiplied  continually  together. 

5.  When  shillings,  pence  and  farthings  are  given,  they  must  be  re- 
duced to  the  decimal  of  a   pound  by  Cases  II.    or   III.    in   Decimals, 
page  82.     When  cents  and  mills  are  given,  there  is  no   need  of  re- 
duction, as  they  are  in  their  nature  the  decimals  of  a  dollar. 

CASE  I. 

When  the  principal,  time,  and  ratio  are  given,  to  find  the 

Interest. 

RULE.  Multiply  the  principal,  time  and  ratio  together, 
the  last  product  will  be  the  answer.  Or  the  proposition 
and  rule  are  more  concisely  expressed  thus,  prt.  =  I. 

EXAMPLES. 

1.  What  is  the  interest  of  £.945  10  for  3  years  at  5  per 
cent,  per  annum  ? 

945,5=prineipal, 
,05=ralio. 


,C.141,825=£.141    IT 

Ans.  £.141 

NOTE.  When  the  interest  is  for  any  number  of  days  only  ;  multi- 
ply the  interest  of  $1  or  «£.!  for  one  day  at  the  given  rate,  by  the 
principal  and  given  number  of  day?,  the  last  product  will  be  the  an- 


SIMPLE  INTEREST  BY  DECIMALS. 
Table  of  Interest  for  $\  or  £.  1  for  one  day. 


IPerct. 
~ 
4 

Decimals. 

Per  ct. 

Decimals. 

.00008219178 
,00009539041 
,00010958904 
,00012328767 

5 
6 

7 
8 

.00013698730 
,00016438356 
,00019178082 
,00021917808 

The  preceding  table  is  thus  made  ; 

days.  day. 

As  365  :  06  :  :   1   :  ,00016438356 
365  :  03  •  :  1  :  ,00021917808,  &e. 

2.  What  is  the  interest  of  g240  for   120  days   at  4  per 
i'ent.  per  annum  ? 

,00010958904X240X120=,003,13,6,1 6435200. 

Aus.  $3,15,6. 

CASE  II. 

Whm  the  principal,  rate,  and  time  are  given,  to  find  the 
amount. 

RULE.  Multiply  the  principal,  rate,  and  time  together, 
the  last  product  will  be  the  interest,  to  which  add  the  prin- 
cipal, and  the  sum  will  be  the  amount.  Or,  prt.+p.=A. 

EXAMPLE. 

3.  What  is  the  amount  of  $279,50  for  7  years  at  4$  per 
cent,  per  annum  ? 

279,50X,045X7=88,04250-J-279,50=$367,54,2|.  Ans. 

NOTE.  When  there  is  any  odd  time  given  with  whole  years,  re- 
duce the  odd  time  into  days,  and  work  with  the  decimal  parts  of  a 
year  which  are  equal  to  those  days. 

4.  What  will  £273  18  amount  to  in  4  years,  175  days, 
a  3  per  cent,  per  annum  ? 

Ans.  £310  14   13,335080064  qrs, 


SIMPLE  INTERST  BY  DECIMALS. 


193 


Table  of  the  decimal  parts  of  a  year,  equal  to  any  number  of 
days,  and  quarters  of  a  year. 


Days. 

Decimals. 

Days. 

Decimals. 

Days. 

Decimals. 

1 

2 
3 
4 
5 
6 
7 
8 
9 

,002740 
,005430 
,0082:20 
,010959 
,013698 
,016433 
,019178 
,021918 
,024657 

10 
20 
30 
40 
50 
60 
70 
80 
90 

,027397 
,054794 
,082192 
,109589 
,136986 
,164383 
,191781 
,219178 
,246575 

100 
200 
300 
365 

,273973 
,547945 
,821918 
1,000000 

i  year  =,25 
*  .  .  =  ,5 
1  .  .  =,75 

CASE  III. 

Wlien  the  amount,  rate,  and  time  are,  given,  to  find  the 
principal. 

RULE.  Multiply  the  rate  by  the  time,  add  unity  to  the 
product,  for  a  divisor,  by  which  divide  the  amount,  the 
quotient  will  be  the  principal.  Qf  a.  _p 

EXAMPLES. 

5.  What  principal  put  to  interest  will   amount  to  $367 
?54,2§  in  7  years  at  4^  per  cent,  per  annum  ? 

,045x7=,315-fl  =  l,315=divisor. 

367,54,21-4-1,315=279,5=8279,50  Ans. 

6.  What  principal  will  amount  to  £310  14  1  3,35080064 
qrs.  in  4  years,  175  days,  at  3  per  cent,  per  annum  ? 

Aus.  £273  18. 

CASE  IV. 

When  the  amount,  principal,  and  time  are  given,  to  find  the 

rate. 

RULE.  Subtract  the  principal  from  the  amount,  divide 
the  remainder  by  the  product  of  the  time  and  principal, 
the  quotient  will  be  the  rate.  Q  ^zEi^R 


rt. 


17* 


COMPOUND  INTEREST  BY  DECIMALS. 

EXAMPLE. 

7.  At  what  rate  per  cent,  will  g279,50  amount  to  $367 
?54j2|  in  7  years  ? 

367,54,2i~27950=8S,04,2| 
279,50x7=1956,50=divisor. 

88,04,25--1956,50=045=4|  Ans, 

CASE.  V. 

WJien  the  amount,  principal,  and  rate  per  cent,  are  given, 
to  find  the  time. 

RULE.     Subtract  the  principal  from  the  amount,  divide 
the  remainder  by  the  product  of  the  rate  and  principal. 


EXAMPLE. 

8.  In  what  time  will  g279,50  amount  to  §367,54,2^  at 
4  §  per  cent.  ? 

367,54,25—  -279,50=  88,04,25=dividend. 
279,50X,045=  1  2,5775=  divisor. 
88,04,25-r-12,5775=7  years.  Ans.  7  years. 


COMPOUND  INTEREST  BY  DECIMALS. 

Let  A=the  Amount. 
P=        Principal. 
T=        Time. 

R=        Ratio,  that  is,  the  amount  of  gl  or  £.1  for  a 
year,  at  any  given  rate. 

NOTE.  For  rules  to  find  the  ratio,  also  a  table  showing  the 
amount  of  $1  or  £.1  from  1  to  10  years,  at  4,  4£,  5  and  6  per  cent, 
per  annum,  with  rules  for  its  construction,  see  Compound  Interest, 
page  151. 

CASE  I. 

When  the  principal,  time,  and  ratio  are  given,  to  find  the 

amount. 

RULE.  Raise  the  ratio  to  a  power,  denoted  by  the  giv- 
en number  of  years,  by  which  multiply  the  principal,  and 


COMPOUND  INTEREST  BY  DECIMALS.          495 

the  product  will  be  the  amount,  from  which  subtract  the 
principal,  the  remainder  will  be  the  Compound  Interest. 
Or  p.Xr'.=A. 

EXAMPLE. 

1.  What  is  the  amount  of  $225  for  3  years  at  5  per 
cent,  per  annum  ? 

1,05X1,05X1,05=1,157625X225=260,465625. 

Ans.  $260,46,5. 

NOTE.  The  raising  of  the  ratio  to  a  power,  denoted  by  the  num- 
ber of  years  given  in  the  question,  being  extremely  tedious,  the  ta- 
ble, alluded  to  above,  will  greatly  facilitate  the  operations  in  Com- 
pound Interest  by  Decimals. 

CASE  II. 
When  the  amount,  rate,  and  time  are  given,  to  find  the 

principal. 

RULE.  Divide  the  amount  by  the  product  of  the  ratio, 
raised  to  a  power,  denoted  by  the  given  number  of  years, 
the  quotient  will  be  the  principal.  Qr  a-  _p 

rr. 

EXAMPLE. 

2.  What  principal,  being  put  to  interest,  will  amount  tt 
$260,46,5,625  in  3  years,  at  5  per  cent,  per  annum  ? 

l,05xl,05Xl,05=l,157625=divisor. 
$260,46,5,625-1 ,1 57625=225.  Ans.  $225. 

CASE  III. 
When  the  principal,  amount,  and  time  are  given,  to  find 

the  ratio,  or  rate  per  cent. 

RULE.     Divide  the  amount  by  the  principal,  the  quotient 

will  be  the  ratio  raised  to  a  power,  denoted  by  the  given 

time ;    find   the   root    of   this  power,  and  it  will  be  the 

ratio.       Or±=rtB    which,  being  extracted  by  the  rule  in 

Evolution,  will  be  the  ratio. 

EXAMPLE. 

3.  At  what  rate  per  cent,  per  annum,  will  $225  amount 
to  $260,46,5,625  in  3  years  ? 

260,46,5,625-5-225=1,157625,  the  cube  root   of  which,  it 
being  the  3d  power,  denoted  by  the  3  years,  gives  1,05=5. 

Ans.  5. 


106  COMPOUND  INTEREST  BY  DECIMALS. 

CASE  IV. 

When  the  principal,  amount.,  and  rate  are  given,  to  find  the 
time. 

RULE.  Divide  the  amount  by  the  principal,  the  quotient 
will  be  the  ratio,  raised  to  a  power  denoted  by  the  given 
number  of  years,  which  being  continually  divided  by  the 
ratio  till  nothing  remains,  the  number  of  these  divisions 
will  be  the  time.  Or  — =rt.  which  must  be  divided  aceor- 

ing  to  the  rule. 

EXAMPLE. 

4.  In  what  time  will  $225  amount  to  $260,46,5,625  at  5 
per  cent.  ? 

260,46.5,625—225=1 ,1 57625. 

1,157625^1,05=1,1025-7-1,05  =  105-5-1,05  =  1,05. 
The  number  of  divisions  being  three  gives  3  years. 

Ans.  3  years. 


SHORT  AND  PLAIN 


SYSTEM 


BOOK-KEEPING, 


CALCULATED   FOR   THE    USE   OE 


RETAILERS,  MECHANICS  AND  FARMERS. 


BOSTON,  SEPTEMBER,  1818, 


BOOKKEEPING. 


BOOK-KEEPING  is  the  art  of  recording  mercantile 
transactions. 
Two  methods  have  been  generally  adopted,  viz; 

1.  Single  entry. 

2.  Double  entry,  commonly  called  the  Italian  method. 
The    method   by   single  entry   is    used  principally    by 

traders  in  retail  business,  and  is  calculated  to  answer  all 
the  purposes  of  the  mechanic  and  farmer,  that  a  just  and 
exact  state  of  their  less  extensive  pecuniary  concerns  may 
at  any  time  be  known. 

As  this  method  is  by  much  the  more  concise  and  simple, 
it  will  be  explained  first,  that  the  scholar  may  have  a  dis- 
tinct view  of  the  subject,  and  be  better  prepared  to  com- 
mence the  more  complicated  and  perfect  method  by  double 
entry. 

Single  entry  requires  two  principal  books,  viz; 
£,      1.  The  Waste,  or  Day-Book. 
2.  The  Leger. 

NOTE.  There  are  several  other  books  used  by  Merchants,  for  a 
description  of  which,  see  Double  entry. 

The  form  of  the  Waste-Book. 

This  book  is  ruled  with  two  columns  on  the  right-hand 
for  dollars  and  cents,  and  one  column  on  the  left  for  insert- 
ing the  folio  of  the  Leger,  to  which  the  account  is  trans- 
ferred. It  is  ruled  with  a  top  line,  on  which  is  written 
the  month,  date  and  year. 

The  articles  are  separated  from  each  other  by  a  line, 
and  the  transactions  of  one  day  from  those  of  another  by  a 
double  line,  in  the  centre  of  which  is  the  day  of  the  month. 

For  a  better  description  of  the  Waste- Book,  see  the 
specimen  annexed. 


BOOK-KEEPING. 


The  use  of  the  Waste-Book. 

This  book  commences  with  an  inventory,  containing  all 
the  ready  money,  notes,  goods,  and  every  other  kind  of 
property,  owned  by  the  merchant;  als»  all  the  debts  due 
by  him  to  others.  Then  follows  a  particular  detail  of 
every  transaction  in  trade,  by  which  new  debts  are  con- 
tracted, or  former  ones  discharged;  the  whole  related  in 
a  concise  and  simple  style,  in  the  order  of  time,  in  which 
they  occur,  with  ihe  quantities  and  prices  of  the  goods, 
purchased  or  sold,  with  every  circumstance,  necessary  to 
render  the  transaction  so  plain  and  intelligible,  that  satis- 
factory information  may  be  readily  given  to  any  interested 
inquirer. 

It  is  of  the  greatest  importance,  then,  that  the  Waste- 
Book  be  kept  wiih  particular  accuracy,  as  it  contains  all 
the  materials  composing  tfie  Leger.  Moreover,  in  cases 
of  disputed  accounts,  this  book  is  exhibited  to  judges,  and 
referees  for  inspection,  that  they  may  ascertain  the  cor- 
rectness of  the  entry,  as  well  as  the  nature  of  ihe  demand, 
and  be  enabled  to  form  an  equitable  decision  between  the 
parties. 

In  entering  an  article  in  the  Waste-Book,  the  following 
circumstances  should  be  carefully  observed;  viz. 

1.  The  date,  and  on  the  top  of  each  page,  the  merchant's 
place  of  residence. 

2.  The  person  with  the  title  Dr.  or  Cr.  annexed,  as  he 
may  become  Dr.  or  Cr.  in  the  transaction.* 

3.  The  part  of  the  transaction  which  belongs    to    the 
merchant. 

4.  The  terms  of  payment. 

5.  «The  quantity,  quality,  mark,  &e.  of  the  article. 

6.  The  price. 

7.  The  amount,  in  the  money  columns. 

8.  The  folio,  or  page,  to  which  the  article  is    refered 
in  the  Leger. 

In  the  Waste-Book,  the  name  of  the  person,  with  whom 

•  the  merchant  has  dealings,  is  written  over  the  account  in 

a  large  round  hand,  or  text,   with  the  term  Dr.   annexed 

when  he  receives  any  thing,  but  with  the  term  Cr.  when  he 

(the  customer)  pays,  gives  or  parts  with  ai?y  thing. 

The  titles  of  Dr.  and  Cr.  may  be  easily  distinguished  by 
the  following  rules  :  viz. 

*  The  term  u  transaction"'  is  applied  to  all  mercantile  business, 


BOOK-KEEPING. 

1.  The  person  to  whom  goods  are  sold  on  credit,  is  Dr*t9 
the  goods  expressing  the  quantity  and  price.      See  Day- 
Book,  January  12,  James  M  HUMID,  &c. 

2.  The  person,   of  whom  goods  are  bought  on  credit,  is 
Cr.  by  the  goods,  expressing  the  quantity  and  price.     See 
Day-Bonk,  January  22,  Rufus  Perkins,  Cr.  &e. 

3.  The  person,  to  whom  money  is  paid,  is  Dr.  to  cash, 
mentioning  whether  in    full  or  in  part.     See  Day-Book, 
Januaiy  31  and  April  27.  Amos  Penniman,  Dr. 

4.  The  person,  from  whom  money  is  received  is  Cr.  hy 
cash,  mentioning  whether  in  full,  or  in  part.     See  Da\- 
Book,  January  25  and  March  4.  John  Grant,  Cr. 

5.  The  person,  to  whom  the  merchant,  in  any  way  he- 
comes  indebted,  is  entered  Cr. 

6.  The  person,  who  in  any  way  becomes  indebted  to  the 
merchant,  is  entered  Dr. 

7.  The  Receiver  is  Dr.  and  the  Giver  is  Cr. 

8.  In    Dr.    Out    Cr. — The  initials  of  which  form  the 
word  idoc,  which  may  assist  the  scholar's  memory. 


THE  LEGER. 

THE  Leger  is  the  merchant's  principal  book,  as  in  it  are 
collected  the  scattered  accounts  of  the  Waste-book,  and 
disposed  in  spaces  assigned  for  them  ;  each  with  the  Debt- 
or placed  on  one  side  of  the  folio,  and  the  Creditor  of  the 
same  account  on  the  opposite  side  of  the  same,  folijj,  by 
which  disposition  the  several  transactions,  connected  with 
each  account,  appear  together  at  one  view. 

TJte  form  of  the  Leger. 

Each  folio,  or  page  of  the  Leger  is  ruled  with  a  top  line, 
on  which  is  writ  tea  the  title  of  the  account,  and  marked 
Dr.  on  the  left  hand,  for  receiving  all  the  debited  articles, 
and  on  the  right  Cr.  for  receiving  all  the  credited  articles 
of  the  Waste  book.  On  the  right  hand  of  both  Dr.  and  Cr. 
sides  are  ruled  two  columns  for  dollars  and  cents ;  one 
column  for  the  folio  of  the  Waste-book,  and  two  on  the  left- 
hand  margin  for  the  month  and  date. 


BOOK-KEEPING. 

The  Leger  has  an  index,  in  which  the  (ides  of  the  ac- 
counts are  arranged  under  their  initial  letters,  with  the 
number  of  the  folio  in  the  Leger,  where  the  account  may  be 
found. 

Rule  for  Posting  the  Leger. 

Enter  the  several  transactions  on  the  13r.  or  Cr.  side  in 
the  Leger,  ^as  they  stand  debited  or  credited  in  the  Day- 
book. 

NOTE.  When  several  person!?  or  things  are  included  in  the  same 
transaction, they  are  distinguished  by  the  term,  "Sundries." 

Balancing  Accounts. 

When  all  the  transactions  are  correctly  posted  into  the 
Leger,  each  account  is  balanced  by  subtracting  the  less  side 
from  the  greater,  entering  the  balance  on  the  less  side,  by 
which  both  sides  will  be  made  equal.  The  balances  being 
added  to  the  cash  on  hand  and  the  value  of  the  goods  un- 
sold, the  sum  is  the  net  of  the  estate,  which  compared  with 
the  stock  at  commencing  businessexhibits  the  profit  and  loss. 

NOTE.  When  the  place  assigned  for  any  person's  account  i?  filled 
with  items,  the  person's  name  must  not  be  entered  a  second  time,  but 
may  be  transferred  to  another  page  in  the  following  manner,  viz.  Add 
up  the  columns  on  both  sides,  and  against  the  sum  write,  u  Amount 
transferred  to  folio  — "  inserting  the  number  of  the  folio  where  the 
new  account  is  opened.  After  titling  the  new  account  and  entering 
the  number  of  the  folio  in  the  index,  write  on  the  Dr.  side  of  the  new 
account,  u  To  amount  brought  from  folio  — "  inserting  the  number 
of  the  folio  from  which  the  old  account  was"  brought,  and  on  the  Cr. 
side  "  By  amount  brought  from  folio  — "  inserting  also  the  folio 
where  the  old  account  was ;  and  place  the  sums  in  the  proper  col- 
umns. See  the  accounts  of  Trask  folio  2  and  3. 

When  the  first  Leger  is  filled  up,  a  new  one  may  be  opened  as  fol- 
lows, viz.  At  the  end  of  the  preceding  Leger,  draw  out  a  balance  ac- 
count, entering  the  debits  and  credits  on  their  respective  Dr.  and  Cr. 
side  and  transfer  eaclf  unbalanced  account  to  its  respective  Dr.  or 
Cr.  side  to  the  new  Leger.  The  first  Leger  anay  be  marked  A,  the 
second  B,  and  so  on  in  alphabetical  order« 


18 


JOURNAL. 


Boston,  January  i,  1817. 


Inventory  of  ready  money,  goods,  and  debt 
due  to  Aaron  Richardson,  merchant,  Boston 

Money  on  hand  ....       $740 

John  Grant  owes  me       ....         140 
Thomas  Moore         .....         175 
William  Young        .....         224* 
75  yards  broadcloth  a  3$  .  225 

121$  yards  of  linen  a  ,75  .  91,31 

20  cwt.  sugar  a  $10,75  .         .         .         215 

800  Ib.  coffee  a  ,20          .         .         .         .         160 


List  of  debts  owed  by  the  said  Aaron  Rieh 
ardson. 

To  Thomas  Andrews,  as  per  account  .         $32( 

Amos  Penniman  ....  7i 

James  Trask  132 


David  Eaton,  Dr. 

To  5  yards  broadcloth 

6  do.  linen 
20  Ib.  coffee 


a  $4,25 
a       ,80 

a       ,29 


12- 


James  Munson,  Dr. 
To  8  yards  broadcloth 

2  cwi.  sugar 
30  Ib.  coffee 


a  $4,25 
a    12,7 


,29 


15 


Thomas  Andrews.  Dr. 

To  Cash,  paid  him  in  part 


•22. 


in  f  us  Perkins,  Cr. 

By  3  chests  hyson  tea  containing  2301b.  net,  a  $1,20 
3  do.  bohea  tea  containiag  2701b.  net  a  ,75 


N.  B.  By  single  entry  goods  bought  are  entered  either  in  an  in- 
nice  book,  kept  for  that  purpose,  or  posted  immediatdv  into  the 
egrer,  from  the  invoices  or  bills  of  parcels.  This  mode,  howev- 
r,  is  not  adopted  here,  but  credited  the  seller  at  the  time/  and 
"terward*  transferred  to  his  accnunt  in  the  Leger. 


c. 


1970 


31 


530 


31 


68 


140 


478 


2]        %  JOURNAL. 

Boston,  January  25,  1817- 


203 


L.  F. 

3 

John  Grant,  Cr. 

By  Cash  received  from  him  in  part 

op 

$- 

32 

C, 

3 

James  Anderson,  Dr. 
To  6  yards  linen                  ...» 

a     ,80 
a     ,29 

31 

10 

60 

Amos  Penniman,  Dr. 

To  Cash,  paid  him  in  part 

40 

1 

Joseph  Hurd,  Dr. 

To  25lb.  hyson  tea         .... 
2£  yards  broadcloth 
14  Ib.  sugar              .... 

a     $1,40 

a       4.75 
a          ,10 

6 

49 

11 

1 

Benjamin  Gould.  Dr. 

To  40  Ib.  bohea  tea         ..... 
12  Ib.  hyson                 .... 
50  Ib.  coffee                 .... 

a       ,85 
a  $1,40 
a       ,29 

in 

X 

65 

30 

1 

Jonathan  May,  Cr. 

By  1  hhd.  molasses,  containing  110  gallons 
1  pipe  of  gin,  containing  124  gallons 
20  qumtals  fish             .... 

IT 

a       ,45 
a  $1,75 

a     8,25 

331 

50 

2 

Thomas  Chandler,  Cr. 
By  2  boxes  candles,  containing  901b. 
80  Ib.  mould  do  

a  ,19 
a  ,25 

«A 

37 

10 

2 

Thomas  Moore,  Cr. 

By  Cash  received  from  him  in  full 

o- 

175 

1 

David  Eaton,  Dr. 
To  75  Ib.  coffe$     .         ,         . 

a        ,28 

3  14  Ib.  sugar 

a  $12,50 

31 

94 

JOURNAL, 


Boston,  February  28,  1817- 


JL.  F. 

1 

David  Eaton,  Cr. 

By  Cash,  in  part  on  account 

March  1 

. 

.  $. 
25 

C 

3 

John  Grant,  Cr. 

By  Cash,  received  from  him  in  full     . 
2 

. 

108 

G 

James  Dean,  Dr. 

To  8  Ib.  candles    ..... 
12  Ib.  coliee        
7  Jb.  sugar       ..... 

a         ,22 
a         ,29 
$1 

10 

6 

24 

4 

Wiliiam  Greenwood,  Dr. 
To  24  Ib.  coffee         .... 
3£  Ib.  bohea  tea          ... 
10  Ib.  candles       .... 

a     ,29 
a     ,86 

a     ,22 

1P 

12 

1? 

2 

James  Traxk,  Dr. 

To  Cash,  paid  him  in  full  . 

'  .  ..                           07 

. 

132 

o 

«? 

Rufiis  Perkins,  Dr. 
To  12  yards  broadcloth 
cash,  paid  him  on  account 

Q1 

a      $4,75 
a  $149 

206 

4 

Jonathan  Boylston,  Dr. 

To  42  Ib.  susrar" 
34  Ib.  coffee 
1  3-|  Ib.  bohea  tea 
8  gals,  gin              • 

i 

a           ,15 
a           ,29 
a           ,85 

a       $2,25 

45 

85 

3 

John  Grant,  Dr. 
To  14  Ib.  sugar              .... 
10^-  gallons  molasses 
4  gals,  gin              .... 
4  Ib.  candles 

a          ,15 
a           ,55 

a       $2,25 
a          ,22 

17 

62 

4 

William  Greenwood,  Cr. 

By  Cash,  received  from  him  on  account 

- 

10 

<i 


UM/<MI,  April  15/1817. 


I,.  F 

I 

James  Trask,  Cr. 
3y  1  hhd.  rum,  containing  117  gals.               a           ,95 
1  pipe  brandy,  containing  126  gals.          a       $2,10 
1  pipe  Madeira  wine,  cont'g.  132  gals,     a       3 

18 

$. 

771 

C. 

75 

i 

William  Bradley,  Cr. 

8y  124  gallons  winter  strained  oil         .         a           ,95 

OQ 

117 

80 

4 

William  Young,  Cr. 

By  Cash,  received  from  him  in  full 
04 

224 

2 

Thomas  Andrews,  Dr. 

To  Cash  paid  him  in  full     ..... 

180 

q 

Amos  Penniman,  Dr. 

To  Cash,  paid  him  in  full                                : 
30 

38 

James  Anderson,  Dr. 

To  10  guls.  oil         .....            $1,10 
8  yds.  broadcloth               ...         a      ,75 
°14  Ib.  coffee                 ....         a       ,29 
1  i  quintal  fish                  .         .         .         a   $5 

Mi-TV   ° 

W 

21 

1 

David  Eaton,  Cr. 

3y  Cash,  received  from  him  on  account 

5_ 

30 

1 

Fames  Munson,  Cr. 

5y  Cash,  received  from  him  on  account 

55 

3 

iufus  Perkins,  Dr. 

To  15^  yds.  linen             ....         a       ,95 
28  Ib.  cheese               ....         a       ,'20 
Cash,  paid  him  on  account          .        .         $250 

-\a 



56 

3 

'ames  Anderson,  Cr. 

3y  Cash,  received  from  him  on  account 

1C 

60 

1 

roseph  Hurd,  Cr. 

Jy  Cash,  received  from  him  on  account            . 

10 

45 

1 

'nnathan  May,  Dr, 
?o  Cash,  paid  him  in  full 

18* 

331 

'•C 

20(5 


JOURNAL. 

Boston,  Maij  £0,   1817. 


JA  F. 

$• 

0. 

1 

James  Munson,  Dr. 

To  20  Jb.  coffee               ....         a 

,29 

24  yds.  linen             ....         a 

,95 

10  gallons  oil             ....          a 

§1,10 

1;£  quintal  iish          ....         a 

4,75 

47 

91 

05 

4 

William  Greenwood,  Dr. 

To  1-2^  Ib  coffee             ....         a 

,29 

7ib.   sugar                ....         a 

$1 

4  J  Ib.  hyson  tea               ...         a 

1,40 

5  gals,  oil                  ....         a 

1,10 

4  gals,  molasses               .         .         .         a 

,55 

oo 

18 

27 

2 

Thomas  Chandler,  Dr. 

To  25  yards  linen             .              •         >4  •             a 

95 

23 

75 

31 

1 

Benjamin  Gould,  Cr. 

V 

By  Cash,  received  from  him  on  account 

54 

50 

7-.     .  _       4 

1 

Benjamin  Gould,  Dr. 

To  24  Ib.  bohea  tea     .             .             .             a 

,85 

12  Ib.  hyson            ...              a 

$1,40 

10  gallons  oil                        ,             .             a 

1,10 

35  Ib.  coffee            ...            a 

,29 

58 

35 

3 

Thomas  More,  Dr. 

To  8£  gals,  molasses                 .             .             a 

,55 

5  gals,  brandy                                                   a 

$2,50 

6  do.  rum              ...            a 

1,25 

24 

67 

1ft 

2 

Thomas  Chandler,  Dr. 

4 

To  12^  Ibs.  hyson  tea              .             .             a.r 

^1,40 

34  Ib.  coffee                                                   a° 

V    ,29 

30  yards  linen                                                  a 

,95 

3  gals.  Lisbon  wine          .            .            o 

1,50 

60 

36 

1 

James  Munson,  Cr. 

By  quarter  cask  cont'g.  34  gals.  Lisbon  wine   a 

$1,25 

42 

50 

JOURNAL. 


207 


Boston,  June  15,  1817- 


JL.  F. 

$.  1C. 

4  William  Young,  Dr. 

To  15  gals,  gin 

a     $2,25 

3  quintals  fish 

a       4,£-: 

18  Ib.  boheatea     . 

a         ,81 

10  gals,  mola&ses    . 

a         ,55 

15  do.  Madeira  wine 

a       3,75 

124 

30 

3 

John  Grant,  Dr. 

To  20  Ib.  mould  candles 

a         ,28 

14  Ib.  hyson  tea     , 

a     $1,40 

l£  cwt.  sugar 

.  ^        <t     12,25 

43 

57 

2 

James  Dean,  Cr. 

By  6  pair  thread  ho»e 

a    gl 

34  pieces  of  Nankinr 

a         ,75 

4  dozen  pairs  silk  hose 

a      2,50 

2  do.  gloves 

a       1,25 

2  dozen  Leghorns 

a       1,75 

24  silk  vests 

a       2 

271 

50 

3 

Amos  Penniinan,  Dr. 

To  5  gallons  Madeira  Wine 

a       $3,75 

1  pair  silk  hose     . 

3 

2  silk  vests 

a         2,50 

1  pair  thread  hose 

1,50 

1  do.  silk  gloves 

1,50 

29 

75 

30 

2 

James  Dean,  Dr. 

To  10  gallons  Madeira 

a       $3,75 

20  Ib.  coffee 

a          ,29 

12  Ib.  hyson  tea 

a         1,40 

3  gallons  oil 

a         1,10 

12  Ib.  mould  candles 

a            ,28 

1  quintal  fish      . 

a         5 

71 

76 

• 

2QS 


JOURNAt. 


Boston,  July  2,  1817. 


t.  F. 

4 
4 

3 

4 

i 
3 

1 

1 
• 

Samuel  Tuekerman,  Cr. 

By  2  pieces  super,  broadcloth,  34yds. 
2  pieces  calicoes,  34  yds. 
1  do.  14£  yds. 
1  piece  bombazet,  30  yds. 
1  piece  black  florentine,  30  yds. 
1  do.  black  lutestring,  20  yds. 
10  ps.  India  bandanna  handkerchiefs 
1^  doz.  Ivory  combs 
2    do.  long  crooked  combs 

3 

a      $4,75 
a         8,50 
7,50 
10 
20 
23 
6 
a        3 
a        2 

$• 
307 

c. 

;s0 

Samuel  Tuekefman,  Cr. 

By  2  dozen  white  tapes 
5000  chapel  needles 
3i  Ib.  coloured  sewing  silk 
3  pieces  white  flannel,  65  yds. 
2  pieces  velvet,  33  yds. 
2  pieces  twilled  coating,  75  yds. 
1  piece  of  satinet,  25  yds. 
4  Ib.  coloured  thread 
5  Ib.  white  thread 
1  piece  of  light  blue  durant,  31  yds. 
1  piece  Scotch  shirting,  70  yds. 
1  piece  coloured  lustring,  18yds. 
2  pieces  Canton  crape 

a          ,80 
S2 
a         5,25 
a           ,50 
a           ,75 
a         1 
10 
a          ,80 
a          ,95 
7,50 
a          ,25 
22 
a       12 

249 

86 

John  Grant,  Dr. 

To  10  gals.  Madeira  wine 
8  do.  rum             .            ... 
2  quintals  fish         . 

in 

a     $3,75 
a       1,25 
a       5 

57 

50 

Jonathan  Boylston,  Cr. 

By  an  order  on  James  Nicholson 
10 

. 

150 

87 

James  Anderson,  Dr. 

To  3£  yds.  superfine  broadcloth 
1  silk  vest          

a    $6,50 
2,50 
a       1,25 
a      3,25 
«       1,50 

' 

2  pieces  Nankins 
3  pair  silk  hose         .... 
2  pair  thread  hese           „        . 

JOURNAL. 


200 


Boston,  July  i5,  1817- 


>  Thomas  Henshaw,  Dr. 

To  65  yards  superfine  broadcloth 
3  Leghorns             .... 
£  dozen  pair  silk  hose 
2  silk  vests       

a    $6,50 
a       2,50 
a       3 
a       2,50 

$- 

72. 

William  Greenwood,  Cr. 

By  his  bill  for  repairs  on  house 
Cash,  received  from  him  on  account 

• 

10 

si 

Samuel  Tuckerman,  Dr. 

To  8  gallons  Madeira 
5  do.  brandy 
10  Ib.  Hyson  tea 
8  gallons  rum 
50  Ib.  coffee 
15  Ib.  mould  candles 
4  cwt.  sugar            .... 

a  $3,75 
a  2,50 
a  1,40 
a  1,25 
a  ,28 
a  ,28 
a  12,30 

133 

John  Grant,  Cr. 

By  Cash,  received  from  him  on  account 
31 

90 

Thomas  Chandler,  Cr. 

By  Cash,  received  from  him  on  account 

. 

90 

Joseph  Bri^ham,  Dr. 

To  4  pieces  Nankins 
64  yards  superfine  broadcloth 
12$  do.  calico             ..... 
5  do.  black  florentine 
1  piece  bandannas 
63  yards  black  lustring 

a    $1,25 
a       6,bO 
a         ,65 
a       1,10 
7 
a       1,50 

77 

James  Trask,  Dr. 

To  Cash,  paid  him  on  account 

. 

350 

* 

JOURNAL. 


Boston,  August  8,  1817. 


David  Eaton,  Dr. 

To  8  yards  superfine  broadcloth 
8  yards  calico           .          .         . 
100  chapel  needles 
1  piece  of  India  bandannas 
3  pairs  thread  hose 
2  do.  silk  gloves 

10 

a     $6,75 
a        ,65 

.'       a       1,40 
a       1,50 

73 

William  Greenwood,  Dr. 

To  8  gallons  molasses 
28  Ib.  sugar        .         .         .     .    . 
5  gallons  rum 
5  Ib.  candles 
2  Ib.  bohea  tea 

it 

a         ,55 

a  $12,25 
a       1,25 
a         .22 
a         ,85 

James  Munson,  Dr. 

To  6$  yds.  superfine  broadcloth 
11  yds.  white  flannel 
i  Ib.  sewing  silk 
6  yards  florentine 
13$  do.  bombazet 

a    $6,75 
a         ,66 
a       1,80 
a       1,10 

a        ,42 

i 

63 

Benjamin  Gould,  Cr. 

By  his  Check  on  Union  Bank 

. 

70 

James  Trask,  Dr. 

To  Cash,  paid  him  on  account 

. 

200 

Thomas  Andrews,  Dr. 

To  13$  yards  calico 
6|  yards  black-  lutestring 
£  pieces  Nankins 
6  pair  silk  hose 
3  pair  silk  gloves 
3  Leghorns 

a        .65 
a     $1,50 
a       1,25 
a      3 
a       1,45 
a      2,50 

51 

10} 


JOURNAL. 


211 


Boston,  August  S8?  1817. 


William  Bradley,  Dr. 

To  1  piece  Canton  crape,  18  yards 
6^  yards  coloured  lutestring 
8j-  do.  satinet 
8  do  velvet                .... 
100  chapel  needles 
i  lb.  coloured  sewing  silk 

a 

a 
a 

a 

$18 
1,50 
,60 

,40 
1,80 

«g 

William  Bradley,  Dr. 

To  2  ivory  combs 
4  lon^  crooked  combs 
(J  yards  bltxck  florentine 
3  pieces  Nankins 
jj  dozen  pciir  silk  hose 
2  pair  silk  gloves 

a 

a 
a 
a 
a 
a 
o> 

,30 
,25 
$1,10 
1,10 
3 
1,45 
2  50 

2  silk  vests       .... 
3^  yds.  superfine  broadcloth 
1  .piece  of  bandanna  handkerchiefs 

*>i 

a 
a 

2,50 
6,75 
7 

Samuel  Tuckerwan,  Dr. 

To  10  gallons  gin           .... 
2  quintals  fish     •    .          ... 
5  gallons  Lisbon  wine 

a 
a 
a 

$2,25 

5, 
1,50 

Srnt    CT 

James  Dean,  Dr. 

To  8  gallons  Madeira  wine 
100  lb.  coffee 
10  lb.  hyson  tea 
15  lb.  mould  candles 
5  gallons  rum            .ft 
4    do.  gin                .  m 
2i  cwt.  sugar           t  . 

»  5     t       - 

a 
a 
a 
a 
a 
a 
a 

$3,75 

,28 
1,40 
,28 
2,50 
2,25 
12,25 

Rufus  Perkins,  Dr.f 

To  10  gallons  Madeira/ 
3    do.  gin             /  . 
1|  quintal  fish      / 
16  lb.  mould  candles 

a 
a 
a 
a, 

$3,75 

2^5 

,2* 

$. 


49 


c, 


55 


76  34 


40 


125  28 


JOURNAL. 


Boston,  September  8,  1817. 


.  F. 

5 

i 
1 

3 
1 

1 
1 

3 

i 

3 

Thomas  Gibson,  Dr. 

To  9  yards  broadcloth                                •         a 
1  silk  vest                      .... 
2  pieces  Nankins             .                              a 
3  pairs  silk  hose                                              a 
4  pairs  silk  gloves             ...         a 

•jo 

$4,50 
2,50 
1,25 
3 
1,45 

60 

<J. 

30 
50 

David  Eaton,  Cr. 

By  Cash,  received  from  him  on  account 

8( 

Joseph  Hurd,  Dr. 

To  7^  yards  calico                 .           .              ~    a 
6  do.  bombazet             ...             a 
2  pieces  Nankins             ...         a 
4  pair  silk  gloves      ....         a 

^                              0>A 

,75 
,42 

$1,2* 

16 

44 
50 

John  Grant.  Cr. 

By  Cash,  received  from  him  on  account 

O/J 

28 

Jonathan  May,  Dr. 

To  3  pieces  Nankins             .                              a 
8^  yards  broadcloth                 .           .         a 
15  yards  linen             ....         a 
6  do.  black  Florentine             .           .           a 
4  pair  silk  gloves      ....         a 

4,75 

,95 
1,10 
1,45 

70 

77 

James  Munsou,  Cr. 

By  his  check  on  the  Union  Bank  for 

Qf) 

. 

112 

Benjamin  Gould,  Dr. 

To  5  gals,  brandy                           *.         .         a 

$2,50 
2,25 
5 
12,25 

l£  quintal  fish           ....         a 
^  cwt.  sugar              ....         a 

38 

19 

Jimes  Anderson,  Cr. 

By  Thomas  Winslow's  acceptance  of  a  draft  for 

50 

>0 

AJM  Penniman,  Cr. 
Sftash,  received  from  him  on  account 

J 

12] 


JOURNAL. 

Boston,  Octobers,  1817. 


L.  F. 
1 

David  Eaton,  Dr. 

To  1  piece  bandannas             , 
6  yds.  coloured  lustring 
7  do.  calico            .... 
200  chapel  needle^       .... 

$7 
a       1,50 

a         ,75 
a        ,40 

* 

4  Ib.  sewinsr  silk 
4  pair  silk  gloves               .           .         . 

a      7,20 
a       1,45 

0 

31 

2 

Thomas  Chandler,  Dr. 

To  10  gals,  brandy         .... 
4  do   mm              .             ... 
3  do.  Lisbon  wine 
8  Ib.  bohea  tea        .... 

a     $2,75 
a       1,25 
a       1,50 
a         ,85 

10 

43 

2 

Thomas  Moore,  Cr. 

By  Cash,  received  from  him  on  account 

. 

4 

4 

William  Greenwood,  Cr. 

By  Cash,  received  from  him  on  account 

. 

20 

3 

James  Trask,  Dr. 

To  15  yards  -white  flannel 
4£  yards  black  lustring 
4  long  crooked  combs     . 
4  pair  silk  hose       .... 
2  silk  vesta      

11 

a         ,66 
a     $1,50 

a         ,25 
a      3 
a      2,50 

35 

2 

James  Dean,  Dr. 

To  7  yards  florentine 
10£  yards  bombazet 
1  dozen  tape             .... 
10  yards  white  flannel 
8^  yards  broadcloth 

------                          16 

a-    $1,10 
a         ,42 
,75 
a        ,66 
a      4,75 

61 

4 

Jonathan  Boylston,  Dr. 
To  12  yards  durant         .... 
8  do.  velvet           .            ... 
20  do.  white  flannel 

a        ,38 
a    $2 
a        ,66 

3C 

JOURNAL. 


[13 


Boston,  October  18,  1817. 


I*.  f 

William  Young,  Cr. 

By  an  order  on  David  Newman  for         ... 

00 

ft 

124 

C. 

25 

4 

Samuel  Tuckerman,  Dr. 

To  Cash  paid  him  on  account 

200 

00 

4 

Jonathan  Boylston,  Cr. 

By  Cash,  received  from  him  on  account 

pc 

99 

o 

Thomas  Henshaw,  Cr. 

By  his  Check  on  Massachusetts  Bank  for 

oq 

75 

00 

t 

Joseph  Bri^ham,  Cr. 

By  Cash,  received  from  him  on  account 

n- 

67 

87 

5 

Thomas  Gibson,  Cr. 

3y  a  bill  on  James  White  a!  10  days 

54 

50 

Thomas  Moore,  Dr. 

To  2  lb.  coloured  thread        .         .         .         a     $1,25 
2  lb.  white  do.             ...           a       1,20 
20  yards  Scotch  shirting             .                    a         ,30 
2  ivory  combs           ....         a        ,30 
4  long  crooked  do.           .                             a         ,25 
4  silk  ve?ts        .....         a      2,50 

00 

22 

50 

1 

Senjamin  Gould,  Dr. 

To  20  gallons  rum          ....         a     $l,2.r- 
10  do.  gin              .             ...         a       2,^r> 
30  yards  Scotch  shirting          ...           .         a         ,30 
900  chapel  needles                                 .         a         ,40 

QA 

50 

10 

1 

fames  Munson,  Dr. 
To  12  gallons  oil           .           ...         a     $1,10 
1  quintal  fish           ....               5 
20  yards  Scotch  shirting                      .         a         ,30 
2  lb.  white  thread           .          -         -         a       1,20 

~9J 

60 

JOURNAL. 


Boston,  November  1.  1817. 


Joseph  Brigham,  Dr. 

* 

To  2500  chapel  needles 

a        ,40 

^  dozen  ivory  combs              .         • 

a'      ,30 

1  dozen  long  crooked  do. 

a        ,25 

3  silk  vests          .... 

a     $2,50 

Is  Ib.  sewing  silk 

a      7 

10  yards  durant 

a        ,38 

36 

66 

3 

I  - 

Samuel  Tuckerman,  Dr. 

V 

To  22  gallons  Madeira  wine 

a    $3,75 

15  do.  Lisbon            .... 

a       1,50 

20  do.  gill             .                               t  » 

a       2,25 

. 

150 

00 

! 

Thomas  Henshaw,  Dr. 

To  9  yds.  white  flannel 

a         ,66 

1  Ib.  coloured  thread 

$1,10 

1  Ib.  white  do. 

1 

3  pieces  bandannas 

a      7 

5  pieces  Nankins 

a       1,25 

13£  yds.  broadcloth 

a      4,75 

4  silk  vests             .           ... 

a      2,50 

10 

108 

23 

Thomas  Gibson,  Dr. 

To  12  pieces  Nankins 

a    $1,25 

1  doz.  silk  hose 

a       3 

3  silk  vests             .                 -  . 

ft       2,50 

5£  yds.  coloured  lustring 

a       1,50 

66 

75 

JO 

David  Ramsay,  Dr.. 

:1o  2  cwt.  sugar              .... 

a  $12,25 

100  Ib.  coffee              .... 

a         ,29 

15  gallons  brandy             .           . 

a       2.75 

10  do.  rum           .... 

a       1,25 

10  Ib.  hyson  tea         .... 

a       1,40 

121  1 

25 

JOURNAL. 


f!6 


Boston,  November  i5,  1817. 


I..  F.  ; 

R.    C. 

1  James  Munscn,  Dr. 

To  1  piece  bandannas 

. 

$7 

14  Leghorns 

a 

2,40 

7  pair  silk  hose 

a 

3,25 

1  dozen  tape 

,75 

1  Ib.  coloured  sewing  silk 

. 

7 

1000  capel  needles 

a 

,40 

2  pair  thread  hose 

a 

1,50 

IP 

78 

10 

4 

William  Young,  Dr. 
To  50  Ib.  coffee 

a 

,29 

20  Ib.  bohea  tea 

a 

,85 

8  gals.  Lisbon  wine 

a 

gl,50 

43 

50 

Oft 

3 

James  Anderson,  Dr, 

To  1  piece  Canton  crape 

.         . 

$18 

16|  yds.  satinet 

a 

,60 

16  do.  velvet 

a 

2 

25  do.  twilled  coating 

a 

1,25 

£  dozen  crooked  combs 

a 

,25 

2000  chapel  needles 

a 

,40 

100 

80 

5 

Joseph  Rrigham,  Dr. 

To  8  ivory  comb? 

a 

,30 

1  dozen  crooked  combs 

n 

,« 

25  yds.  twilled  coating 
1  Ib.  coloured  thread 

a 

1 

2000*<iiapel  needles 

a, 

,40 

2  pieces  bandannas 

a 

7 

59 

11 

4 

Jonathan  Boy  1st  on,  Dr. 

To  3£  sugar 

a 

§12,25 

30  Ib.  coffee 

a 

,29 

10  gallons  molasses 

ft 

.55 

1  quintal  fish 

6 

10  gallons  gin 

a 

2.25 

26  Ib.  bohea  tea 

:: 

106 

67 

161 


JOURNAL. 


Boston,  November  30,  1817. 


L.F. 


2  James  Dean,  Dr. 

To  25  gallons  Madeira 
20  lb.  hyson  tea 
30  lb.  coffee 

2  quintals  fish 
20  gallons  rum 
18  do.  brandy 


William  Greenwood,  Dr. 

To  25  lb.  bohea  tea 
12  gallons  oil 
25  gallons  molasses 
10  do.  brandy 


Amos  Penniman,  Dr. 
To  29£  lb.  coffee 

20  gallons  molasses 
1  quintal  fish 

25  lb.  candles 

15  gallons  oil 


Joseph  Hurd,  Dr. 

To  14^  gallons  molasses 
18  gallons  rum 
59  Ib.  bohea  tea 
10  gallons  oil 
1  quintal  fish 


10 

Benjamin  Franklin,  Dr. 

To  19  gallons  Madeira  wine 

7  Ib.  mould  candles 
*2  0  14  lb.  sugar 
17  gallons  rum 
30  lb.  hyson  tea 
22  gallons  gin 
15  do.  brandy 


a 

83,75 

$• 

. 

a 

1,40 

. 

a 

,29 

.            . 

a 

5 

. 

a 

1,25 

• 

a 

2,75 

214 

r. 

a 

,85 

. 

a 

gl,25 

. 

a 

,60 

• 

a 

2.75 

78 

a 

,29 

. 

,        a 

,60 

. 

. 

S5 

. 

a 

,22 

• 

a 

1,10 

47 

a 

,60 

. 

a 

81,25 

. 

.         a 

,85 

. 

a 

1,10 

• 

• 

5 

97 

a 

83,75 

. 

a 

,22 

. 

.         a 

12,2o 

• 

a 

1,25 

. 

a 

1,40 

. 

.         a 

2,25 

• 

a 

2,75 

252 

[1? 


Boston ,  December  i%,  1817- 


2  James  Dean.  Dr. 

To  13  g-alloii:  , 
31  ib.  cand'^ 
15  gallons  oil 


4j  William  Young,  Dr. 
To  25  gallons  brandy 
22  do.  oil 
35  Ib.  hyson  tea 


g2,25 

,22 

1,10 


15 


a  $2,75 
a  1,10 
a  1,40 


18 


3  John  Grant,  Dr. 

!To  30£  Ib.  bohea  tea 
18  gallons  brandy 
23?  hyson  tea 


1 


a  ,85 
a  g2,75 
a  1,40 


19 


David  Eaton,  Cr. 

By  Cash,  received  from  him  in  full 
20 


jjames  Munson,  Cr. 

i  By  his  note,  dated   this  day,  payable  to  my  order, 
at  90  days,  for  balance  of  his  account 


Thomas  Andrews,  Cr. 

By  David  Standwood's  acceptance  of  a  draft  to  my 
order,  dated  this  day,  payable  at  sight,  for  g51,25 
bein  the  balance  of  his  account 


Rufus  Perkins,  Cr. 
By  Cash  in  full 


John  Grant,  Cr. 

By  Cash,  received  from  him  to  balance  account 


James  Anderson,  Cr. 

By  his  Check  on  Boston  Bank  for 

23 


Amos  Penniman,  Cr. 

By  Cash,  received  from  him  in  full 
^  __—_ 


James  Dean,  Cr. 

By  his  Check  OB  Boston  Bank  for 


63 


82 


141 


95 


108 


33 


75 


51 


54 


108 


102 


48 


271 


19 


54 


16 


25 


85 


38 


48 


80 


55 


18]  JOURNAL. 

Boston.  December  24,  1817. 


219 


L.   F. 

1 

Jimeph  Hurd,  Cr. 

By  Cash,  received  from  him  in  full 

*j. 

in 

v>. 
75 

1 

Benjamin  Gould,  Cr. 
is   Check  on    Manufacturers'    and    Mechanics' 
Bank  at  Boston,  for                ... 

Oj 

8T 

44 

4 

William  Brad  l«-y,  Cr. 

,.v  Cash,  received  from  him  in  full 

' 

8 

09 

1 

.  ,   ..         ^      ,,,  ,.,.                                ^, 
Jonathan  May,  Cr. 
By  Cash  in  full  "  ' 

70 

77 

4 

William  Young.  Cr. 

By  Cash,  receivf  d  from  him  i^  full 
"6 

186 

50 

5 

Thomas  H^u^uau.  Cr. 

By  Cash,  received,  from  him  in  fall        -     . 

105 

98 

320                                          LEGER.                                              [1 

Dr.                     David  Eaton, 

1817. 

JF 

<g. 

C. 

Jan. 

5 

1 

To  Sundries,  as  per  Journal 

3] 

85 

Feb. 

25 

2 

—  Sundries           .... 

31 

94 

Aug. 

8 

9 

—  Sundries           .... 

72 

80 

Oct. 

8 

12 

—  Sundries          .... 

31 

45 

169 

04 

Dr.                  James  Munson, 

1817. 

Jan. 

12 

1 

To  Sundries,  as  per  J. 

68 

20 

May 

20 

5 

—  Sundries 

47 

91 

Aug. 

15 

9j  —  Sundries 

63 

85 

Oct. 

30 

13—  Sundries 

.26 

60 

Nov. 

15 

15 

—  Sundries 

78 
284 

10 
M 

Dr.                    Joseph  Kurd, 

1817. 

Feb. 

3 

2 

To  Sundries,  as  per  J.       . 

49 

11 

Sept. 

15 

11 

—  Sundries          .... 

16 

44 

Dec. 

8 

16 

—  Sundries          .... 

97 

20 

162 

75 

Dr.                 Benjamin  (rould, 

1817. 

Feb. 

6 

2 

To  Sundries,  as  per  J. 

65 

30 

June 

4 

5 

—  Sundries          .... 

58 

35 

Sept. 

30 

11 

—  Sundries          .             . 

38 

19 

©ct. 

2>; 

lo 

—  Sundries         .... 

50 

10 

211 

94 

Dr.                  Jonathan  May, 

1817. 

May 

18 

4 

To  Cash  in  full     .... 

331 

50 

Sept. 

24 

11 

—  Sundries 

70 

77 

»402 

£7 

LEGER. 


Cr. 


1817. 

IJFj    $. 

C. 

Feb. 

28 

By  Casli,  in  part 

3 

25 

May 

2 

—  Cash                 .... 

4 

30 

Sept. 
Dec. 

121—  Cash 
19  Cash,  for  balance 

11 
17 

80 
33 

50 

54 

- 

169 

04 

Cr. 

1817. 
May 

5 

By  Cash,  in  part 

4 

55 

June 
Sept. 

12 

26 

—  34  gallons  Lisbon  wine             .         a    $1,25 
—  Check  on  Union  Bank,  Boston 

5 
11 

42 
112 

59 

Dec. 

20 

—  Cash,  in  full 

17 

75 

16 

! 

1284 

66 

Cr. 

1817. 

15 

By  Cash                .... 

4 

45 

Dec. 

24 

—  Cash  in  full       .... 

18 

117 

75 

f 

!lC2J7§ 

Cr. 

1817. 

j 

May 

Aug 

31 

:o 

By  Cash                 .              ... 
—  His  check  on  Union  Bank 

I 

54 
70 

50 

Dec. 

24 

—  His  check  on  Mechanics'  Bank 

18 

87 

•14 

|211 

194 

Cr. 

1817. 

I  <  b. 

By  Sundries,  as  per  Journal 

21331 

50 

L'er,. 

25  —  <Ja=h  iu  lull 

18 

7077 

I 

I 

402127 

g2£                                          LEGER. 

Dr.                      James  Dean. 

6 
71 
125 
61 
214 
63 

c* 

24 
76 
26 
02 
95 
82 

1817. 
March 
June 
Sept. 
Oct. 
Nov. 
Pec. 

8 
30 
2 
14 
30 
12 

r.p 

3  To  Sundries  as  per  Journal 
6  —  Sundries 
10  —  Sundries 
12  —  Sundries 
16  —  Sundries 
17  —  Sundries 

543 

05 

Dr.                 Thomas  Chandler, 

1817. 
May 
June 
Oct. 

28 
10 
91 

5  To  25  yards  linen           .             .              a     ,95 
5  —  Sundries 
2  —  Sundries        .... 

23 
60 
43 

75 
36 
80 

127 

91 

Dr.                    Thomas  Moore, 

1817. 
Jan. 
June 
Oct. 

1 
6 

26  1 

1  To  balance  on  old  account         , 
5  —  Sundries        .... 
3  —  Sundries        .... 

175 

24 
22 

67 
50 

222 

17 

Dr.                     James  Trask, 

1817. 

March 
Aug. 

13    ; 

}  To  Cash  in  full 
j        Cash  in  part 

Amount  transferred  to  folio  3. 

132 

350 

4821 

- 

Dr.                 Thomas  Andrews, 

1817. 
Jan. 
April 
Aug. 

5     ] 
14    • 
27    1 

To  Cash  in  part 
1  —  Cash  in  full    -           ... 
)  —  Sundries        .             . 

140 
ItfO 
51 

371 

>5 
>5 

223 

Cr. 

C. 

50 

55 

1817. 
June 
Dec. 

3 

By    Sundries  as  per  J. 
By  his  check  on  Boston  Bank 

-TF 

17 

$ 
271 
27] 

543 

05 

Cr. 


1817. 

Feb. 

15 

By  Sundries  as  per  Journal 

2 

37 

10 

July 

31 

—  Cash              .... 

8 

90 

81 

127 

91 

Cr. 


1817. 

Feb. 

«.< 

By  Cash  in  full 

2 

175 

Oct. 

10 

—  Cash               .... 

1'2 

4 

07 

Dec. 

31 

—  Account  at  folio  1  ieger  B. 

42 

•>o 

222 

17 

Cr. 


1817. 

Jan. 
April 

1 
15 

By  balance  on  former  account 
—  Sundries 

\ 

Amount  transferred  to  folio  3. 

9U3J7» 

Cr. 


1817. 

Jan. 

1 

By  stock             .... 

1 

320 

Dec. 

21 

—  D.  Standwood's  acceptance 

17 

51 

-2i 

371 

25 

Dr. 


LEGER. 
Kufus  Perkins. 


31 


1817. 

j>'j 

March 

27 

3  To  Sundries  as  per  Journal 

206 

May    " 

8 

4J  —  Sundries         .... 

270 

56 

Sept* 

5 

10. 

—  Sundries         .             . 

56 

79 

533 

35 

Dr.                        John  Grant,       *  0 

1817. 

Jan. 

1 

1 

To  balance  of  okl  account 

140 

April 

7 

o 

—  Sundries        .... 

17 

62 

June 

20 

6 

—  Sundries        .... 

43 

57 

July 

5 

7 

—  Sundries        .... 

57 

50 

Dec. 

18 

17 

—  Sundries 

108 

19 

3G6J88 

Dr.                   James  Anderson, 

1817. 

Jan. 

28 

2 

To  Sundries  as  per  Journal 

10 

00 

April 

4 

—  Sundries 

5<5 

'21 

July 

12 

7 

—  Sundries           .... 

38 

H7 

Nov. 

:>0 

15 

—  Sundries          .... 

100 

80 

7PJ 

48 

Dr.                   Amos  Pennimun, 

1817. 

Jan. 

31 

2 

To  Cash  in  part 

April 

27 

4 

—  Cash  in  full 

June 

27 

6 

—  Sundries 

75 

Dec. 

5 

16 

—  Sundries 

47 

5i 

155 

30 

Dr.                     James  Trask, 

1817. 

j  o  amount  brought  irom  ioao  2 

482 

Aug. 

24 

9 

To  Cash              .... 

2^0 

Oct. 

12 

12 

—  Sundries         .... 

35 

0* 

Dec. 

31 

—  account  transferred  to  folio  1  leger  B. 

186 

72 

903 

vfc 

LEGER, 


Cr. 


Ibl7. 
Jan. 
Dec. 

22 

By  Sundries,  as  per  Journal 
—  Cash,  in  full 

JF 
1 

17 

$. 
478 
54 

C. 

50 
85 

533 

35 

Cr. 

1817. 
Jan. 
March 
July 
Sept. 
Dec. 

4 
27 
20 
22 

By  Cash  in  part 
—  Cash  in  full 
—  Cash  on  account 
—  Cash  on  account 
—  Balance         .... 

2 
3 
8 
11 
17 

32 
'  108 
90 
28 
108 

50 
3S 

; 

366 

83 

Cr. 

1817. 
May 
Oct. 
Dec. 

12 
1 

22 

By  Cash  on  account 
ornas  Winslow's  acceptance  for 
—  his  Check  on  Boston  Bank 

4 
11 
17 

60 
50 
102 

48 

— 

212 

48 

Cr. 

Jan. 
Oct. 
Dec. 

1 

7 
23 

By  Balance  due  on  old  account 
—  Cash  on  account 
—  Cash  in  full 

1 
11 
17 

78 
28 
48 

50 
80 

155 

30 

Cr. 

1817. 

By  amount  brought  from  folio  2 

903 

75 

903 

TS 

Dr. 


LEGER. 

William  Young, 


1817. 
.Tan. 
June 
Nov. 
De«. 

1 
15 

JF 
1 

6 
17 

To  balance  of  old  account 

224 
124 
43 
141 

C. 

50 
95 

75 

—  Sundries         .... 

533 

Dr.              Samuel  Tuekerman, 

1817. 
July 
Aug. 
Oct. 
Nov. 
Dee. 

23 
31 
20 
3 
31 

1 

8 
10 
13 
13 

133 
40 
200 
150 
33 

90 
46 

_  Cash         

—  Balance  transferred  to  folio  1  Leger  B. 

557 

36 

Dr.              William  Greenwood, 

1817. 
March 
May 
Aug. 
Dec. 

12 

25 
10 

2 

3 
5 
9 
16 

To  Sundries         ..... 

12 

18 
16 

78 

17 
27 
51 
75 

125 

70 

Dr.                Jonathan  Boylston, 

1817. 
jr    March 
Oct. 
Nov. 
Dec. 

31 

16 
27 
31 

15 

To  Sundries 
—  Sundries         .         .         .         .           . 

45 
33 
106 

24 

85 
76 
67 
71 

99 

To  Balance  transferred  to  folio  1,  Leger  B. 

210 

IDr.                  William  ttradley, 

1817.  I     1     | 
Aug.      28  10  To  Sundries          
-  -       29  10        Sundries 

4954 
7634 

LEGER, 


Cr. 


1817. 
April 
Oct. 
Dec. 

20 
18 
-25 

By  Cash  in  full 
—  An  order  on 
—  Cash  in  full 

D.  Newman      . 

JF 

4 
13 

18 

$• 

.224 
124 
185 

t 

25 
50 

533 

75 

Cr. 

1817. 

July 

2 
3 

By  Sundries,  as 
—  Sundries 

per  Journal 

7 
7 

307 
249 

50 

86 

36 

557 

Cr. 

1817. 

April 
July 
Oct. 
Dec. 

10 
IM 
10 
31 

By  Cash 

—  Sundries 
—  Cash 
—  Balance  clat 

jut  trim*.,  to  ibiio  1,  Legtr  b. 

3 

2 

1C 

15 

7 
125 

7  if 
70 

Cr. 

1817. 
July 
Oct. 

10 

21 

By  a  draft  on  J.  Nicholson' 
—  Cash  on  account 

7 
13 

150 
.60 

210 

99 
99 

Cr. 

1817. 
April 
Dec. 

I 

If* 
25 

By  124  gallons  oil 
—  Cash  in  full 

I 

4 
18 

117 

8 

30 

an 

125 

Dr. 


LEGER. 

Thomas  Hens  haw, 


1817. 
July 

Nov. 

IJF 

15    8 
8J14 

1 

To  Sundries 
I  —  Sundries        .... 

• 

$. 
72 
108 

180 

C. 

75 
23 

98 

Dr.                  Joseph  Brigkam, 

1817. 

Aug. 

Nov. 

2 
1 
25 

8 
14 
15 

To  Sundries        .... 
—  Sundries        .... 
—  Sundries        .... 

~~ 
173 

62 
^0 
o5 

87 

Dr.                  Thomag  Gibson, 

1817. 
Sept. 

Nov. 

8 
10 

11 

14 

To  Sundries        .... 
—  Sundries        .... 

60J30 

66J75 

12705 

Dr.                  David  Ramsey, 

1817.        | 
Nov.     |12|14|To  Sundries       .... 

12125 

Dr.               Benjamin  Franklin, 

1817. 
Pec.     (10 

16|To  Sundries        ....                252J82 

Dr.                          Balance, 

1817. 
Pec. 

31 

LF 

2 

4 
5 

5 

5 
5 

To  Thomas  Moore,  due  to  me 
—  William  Greenwood 
—  Joseph  Brierham 
—  Thomas  Gibson         .             , 
—  David  R;imsey 
—  Benjamin  Fraitklin    , 

4? 
79 

106 
72 
121 

252 

675 

50 

% 

55 
25 
82 

00 

LEGER., 


Cr. 


1817. 

JF 

$ 

C. 

Oct. 

00 

By  Check  on  Massachusetts  Bank 

13 

75 

Dec. 

26 

—  Cash  in  full 

18 

105 

98 

180 

98 

Cr. 


1817. 

Oct. 

23 

By  Cash              .... 

13 

67 

87 

Dec. 

31 

—  Balance  due  to  me  transf.  to  folio  1  Leger  B. 

106 

173 

87 

Cr. 


1817. 

Oct. 

25 

By  bill  on  James  White  at  10  days 

13 

64 

50 

Dec. 

31 

—  Balance  due  to  me  transf.  to  folio  1  Leger  B. 

72 

55 

127 

05 

Cr. 


1817. I 
Dec.    |3l|By  Balance  transferred  to  folio  1  Leger  B. 


I         I 

I  121(25 


Cr. 


1817. 


Dec.     |31jBy  Balance  transferred  to  folio  1  Leger  B. 


20* 


I 
252182 


Cr. 

181  ;. 

Dec. 

31 

By  Jonathan  Boylston,  due  to  him 
—  James  Trask 
—  Samuel  Tuckerman 

LF 

4 
3 
4 

23 
1R6 
33 

71 

72 
46 

243 

89 

£30  LEGER.  [1 

LEGER  B. 

Dr.  Thomas  Moore, 

"181871     LF/ j    JJTJC. 
Jan.      II      j  To  balance  at  folio  2  Leger  A.  .         .         |     42|50 

Dr.  William  Greenwood, 

1818.  I     I     I  *~  ~~\ 

Jan.      j   l|     (To  balance  at  folio  4  Leger  A.  .          .         |     79|9.r. 

Dr.  Jotmthau  Boylstoii, 


1818.  '\ 


Dr.  James  Trask, 


Dr.  Samuel  Tuckerman, 

1818. 


.Dr.  Joseph  Brigham, 

Tirnn  |  i  j     [~ 

Jan.      j  1|  [To  balance  at  folio  5  Leger  A.          .         .         (106| 
Dr.  Thomas  Gibson, 


181.8. 
Jan. 


l|     (To  balance  at  folio  5  Leger  A.  |     72(55 


j)r.  David  Ramsey, 


i  i"~ 

Jan.      Mi     |To  balanqe  at  folio  5,  Leger  A.         .         .         |  121|25 
Dr.  Benjamin  Franklin, 


Jan.     I  T     ITo  balance  at  folio  5  Leger  A. 


)  LEGER. 

LEGER  B, 

Cr. 


IJFJ    $.    )C< 
I       I  I 


Cr. 


Cr. 


1818.  j     j  1     I         I 

.Ian.      I   1'By  balance  at  folio  4  L^ger  A.  ..II     24i7l 


Cr. 

1318.  .     ,  Y   i        i 

Jan.      I  IJBy  balance  at  folio  3  Leser  A.  .         .         I 


Cr. 

Jan.      |  l|By  balance  at  folio  4  Leger  A.  !     33146 

Cr. 


Cr. 


Cr. 


Cr. 

T~T 


LEGER. 

(Book-Keeping  by .  single  entry  does  not  show  what  goods  are 
unsold  or  the  profits  or  losses,  except  when  the  transactions  are  very 
few.  The  Leger  containing  nothing  but  the  accounts  of  persons 
dealing  on  credit,  only  shows  the  merchant  what  debts  are  due  to 
him,  and  what  he  owes  to  others. 

If  therefore  he  wishes  to  know  what  goods  remain  unsold  and  what 
his  profits  arid  losses  by  the  whole  or  any  part  of  his  business,  he  can- 
not obtain  this  knowledge  by  single  entry  without  u  taking  account 
of  stock,1'  that  is,  by  weighing  or  measuring  every  article  remaining 
unsold,  which  are  commonly  valued  at  prime  cost.  The  value  being 
added  to  the  money  on  hand,  will  exhibit  the  net  of  the  estate, 
which,  compared  with  the  original  stock,  will  show  the  Profit  and 
Lo?s. 

Hence  it  appears  evident,  that  Book-keeping  by  single  entry  is 
essentially  defective  in  its  not  giving  the  merchant  a  correct  knowl- 
edge of  the  state  of  his  affairs,  without  the  laborious  task  of  u  taking 
account  of  stock,"  which  is  very  subject  to  error,  and  can  afford  no 
adequate  means  either  of  preventing  embezzlement  or  detecting  fraud. 
'  Fortunately,  however,  for  the  wholesale  merchant,  and  the  less 
extensive  trader,  these  objects  are  attained  by  the  Italian  method  of 
double  entry,  as  effectually,  perhaps,  as  the  ingenuity  of  man  can 
devise. 

Every  scholar,  therefore,  who  wishes  to  become  a  complete  ac- 
countant, must  be  conversant  with  that  system,  which  being  upon 
universal  principles,  and  clearly  understood  by  the  pupil,  will  easily 
lead  to  the  invention  of  other  plans  more  conveniently  adapted  to 
any  particular  purpose.) 


238 


UYDEX  TO  1 

A. 

Fol.  i 
Andrews  Thomas       .         .        JB-| 
Anderson  James         .         .         3 

?HE  LEGER. 
B. 

Fol 
Balance     ....         5 
Boylston  Jonathan     .         .         4 
Bradley  William         .         •         4 
Brigham  Joseph          .         .         5 

c. 

Chandler  Thomas 

2 

D. 

'Dean  James 

/ 

2 

E. 

Eaton  David 

1 

F. 

Franklin  Benjamin     . 

5 

G. 

Grant  John 
Gould  Benjamin 
Greenwood  W. 
Gibson  Thomas 

3 
1 
4 
5 

H. 

'Hurd  Joseph 
Henshaw  Thomas 

1 

M. 

Munson  James  .         .         » 
May  Jonathan   . 
Moore  Thomas 

1 
1 
2 

P. 

Perkins  Rufus    . 
fenniman  Amos 

3 
3 

H. 

Ramsey  David           » 

5 

T. 

Trask  James     .         .         -2,  X 
Tuckerman  Samuel    .         .         4 

Y. 

Voung  William 

INDEX 
A. 

4 

—  • 

TO 

i  ^ 

LEGER  B. 
B. 

Brigham  Joseph 

Boylston  Jonathan     . 

1 

1 

E. 

F. 
Franklin  Benjamin     .     .    . 

1 

G. 

Gibson  Thomas 
Greenwood  William 

l 
l 

M. 

Moore  Thomas 

1 

R. 

Ramsey  David  .. 

1 

T. 

Trask  James 

\  Tuckeriuau  Saiuuel    . 

1 

\ 

NEW  AND  CONCISE 

SYSTEM 


OF 


BOOK-KEEPING, 

BY 

EXTRT1-, 

FOR   THE  USE  OP 

WHOLESALE,  DOMESTIC  AND  FOREIGN 
TRADE, 

AS    CONDUCTED   IN   THF, 

UNITED    STATES, 

The  whole  designed  for  the  use  of  Schools  and 
BY  D.  STANIFORD,  A.  M. 


BOOK-KEEPING. 


EVERY  mercantile  transaction  has  two  parts,  or  be- 
longs to  two  accounts,  and  requires  its  distinct  entry  on  the 
Dr.  of  the  one,  and  on  the  Cr.  of  the  other,  to  show  the 
change  of  property.  From  this  circumstance  arises  the 
distinguishing  title  of  this  method  by  Double  Entry. 
The  art  of  Book-Keeping  by  Double  Entry  consists, 

1.  In  recording,  correctly  and  intelligibly,  the  transac- 
tions in  the  several  books.         a 

2.  In  transferring;  the  several  accounts  from  one  book  to 
another,  with  the  corresponding  Drs.  and  Crs. 

3.  In  the  method  of  balancing  and  closing  the  accounts, 
There  are  three  primary  books  used  ;  viz. 

1.  The  Wa«te,  or  Day  Book. 

2.  The  Journal. 

3.  The  Leger. 

The  secondary  or  auxiliary  books  are, 


1.  The  Gash 

2.  Bill 

3.  Invoice 

4.  Sales 

5.  Account-current 

6.  Commission 


•Book. 


7.  Sbip's-account' 

8.  Expense 

9.  Letter 

10.  Postage 

11 .  Receipt 

12.  Check 


.Book. 


To  which  may  be  added,  the  Numero,  or  Ware-house  Book, 
and  Memorandum  Book. 

Part,  or  the  whole,  of  the  preceding  books,  are  used  by 
merchants,  as  the  extent  and  nature  of  their  business  ma* 
require. 

WASTE-BOOK. 

FOR  the  form  and  use  of  this  book,  see  (he  Waste,  or 
Day  Book,  in  Single  Entry. 


BOOK-KEEPING.  $37 

THE  JOURNAL. 

THE  Journal  is  a  fair  transcript  of  all  the  transactions, 
recorded  in  the  Waste  Book,  compiled  in  the  same  order, 
but  differently  expressed.  Here  the  two  parts,  which  be- 
long to  every  transaction,  in  the  Waste,  are  clearly  distin- 
guished by  their  proper  titles  with  their  mutual  relation  of 
Dr.  and  Cr.  to  facilitate  their  transfer  to  their  separate  ac- 
counts in  the  Leger. 

The  form  of  this  book  is  similar  to  the  Waste,  with  this 
only  exception,  that  on  the  left  hand,  there  are  two  col- 
umns for  references  to  the  folio  of  the  account  in  the  Leger. 
the  first  for  the  Dr.  and  the  second  for  the  Cr.  See  speci- 
men annexed. 

An  experienced  book-keeper  can  easily  dispense  with  either  the 
Waste  book,,  or  Journal;  but  the  young  book-keeper  needs  them 
both,  for  simplicity  and  clearness. 

The  art  of  Book-keeping,  by  the  Italian  method,  wholly 
depends  on  a  correct  discrimination  of  the  Dr.  and  Cr.  of 
each  transaction.  The  mode  of  ascertaining  them,  in 
double  entry,  is  the  same,  in  effect,  as  in  single.  But  here 
things,  as  well  a*  persons,  are  made  Drs.  and  Crs.  and  one 
thing,  or  person,  is  made  Dr.  to  another  thing,  or  person, 
asCr. 

DEBTOR  ^JTD  CREDITOR. 

The  following  rales,  for  distinguishing  the  titles  Dr. 
and  Cr.  with  the  explanations  and  notes,  will  greatly  assist 
the  young  book-keeper  in  making  the  Journal  entries  from 
the  Waste  book  and  posting  from  the  Journal  to  the  Leger. 

RULE  I.  When  goods  are  sold  on  credit,  the  Purchaser 
is  Dr.  to  goods  ;  and  Goods  Cr.  by  the  purchaser.  See 
Waste  and  Journal,  Jan.  2.  Sold  Charles  Lee,  sugar. 

Explanation  1.  As  the  sugar  is  sold  but  not  paid  for,  Charles  Lee 
must  be  made  Dr.  to  sugar ;  and  Sugar  Cr.  by  Charles  Lee,  for  the 
quantity  and  price. 

NOTE  1  In  all  cases  of  selling,  the  goods,  sold  and  delivered,  are 
Cr.  but  the  Dr  varies  according  to  the  terms  of  sale. 

RULE  II.  When  goods  are  sold  for  cash,  make  Cash  Dr. 
to  goods  sold  ;  and  Goods  Cr.  by  Cash.  W.  and  J.  Jan.  7. 
Sold  rum  for  cash. 

Explanation  2.  As  the  rum  is  sold,  and  the  money  received  at 
the  time,  it  is  not  necessary  to  know  to  whom  it  was  sold,  but 
the  money  received,  that  is,  Cash  is  Dr.  to  the  rum,  for  its  value } 
and  the  Rua  Cr.  by  Cash  for  the  quantity  and  price. 


BOOK-KEEPING 

« 

RULE  III.  When  goods  are  sold  for  part  cash  and  part 
0.11  credit,  make  Sundries  Dr.  to  goods  sold;  viz.  Cash,  for 
the  sum  received,  and  the  Purchaser,  for  the  rest ;  also 
Goods  sold  Cr.  for  the  whole  amount.  W.  and  J.  Sept.  27, 
Sold  Winslovv  Lamb,  tea. 

Expl.  3.  This  case  is  the  reverse  of  Feb.  22.  Here  Sundries  are 
Dr.  to  tea;  viz.  Cash,  for  fne  money  received,  and  W.  Lamb,  for 
the  rest ;  then  Tea  is  Cr.  by  sundries. 

RULE  IV.  When  goods  are  sold  for  part  cash  and  partbills, 
make  Sundries  Dr.  to  goods  sold;  viz.  Cash,  for  the  money 
paid,  and  Bills  receivable*  for  the  rest,  or  value  of  the  bill ; 
also  the  Goods  sold  Cr.  by  sundries,  specifying  the  price 
and  quantity.  W.  and  J.  Jan.  27.  Sold  A.Eastman,  lands, 
for  cash  and  bills. 

Extol.  4.  In  this  case  make  Sundries  Dr.  to  laad  for  its  value ; 
TJZ.  Cash,  for  the  sum  received,  and  Bills  receivable,  for  the  rest ;  also 
Land  Cr.  by  sundries  for  the  same  value. 

NOTE  2.  If  you  sell  a  house,  or  ship,  &c. ;  make  the  entry  as  in 
selling  goods  ;  viz.  Cash,  Buyer,  &c.  ;  Dr.  to  house,  ship,  &c. ;  for 
the  value.  Aug.  18.  Aug.  19.  Dec.  25. 

RULE  V.  AVhen  goods  are  sold,  and  payment  received  by 
a  bill  or  draft  on  another  person,  make  Bills  re  civ  able  Dr. 
fo  goods  sold;  and  Goods,  stating  the  pr-c-e  and  quantity, 
Cr.  by  bills  receivable,  expressing  on  \vhom  drawn.  W.  8c 
J.  Feb.  25.  Sold  N.  Freeman  linen  for  a  bill  on  A  Young. 

Expl.  5.  Here  Bills  receirable  are  Dr.  to  linen,  and  Lintn  Cr. 
fcy  bill  on  A.  Young,  for  600  yards  a  $1.20. 

NOTE  3.  When  several  sorto  of  goods  are  sold,  there  will  be  sun- 
dry Crs.  viz.  the  several  sorts,  each  for  its  value  ;  but  the  Drs.  will 
be  the  same  as  in  Note  3.  '  Thus.,  dish  Dr,  to  sundries,  if  sold  for 
cash,  Buyer^  if  on  time,  Bills  Ttztivable,  if  for  bill. 

RULE  VI.  Goods  bought  for  ready  money,  are  Dr.  to 
Cash,  and  Cash  Cr.  by  the  goods.  W.  and  J.  Jan.  15. 
Bought  port  wine  for  cash. 

Expl.  6.  The  port-wine  being  bought,  and  the  money  paid,  Port- 
wine  must  be  nu.de  Dr.  to  Cash,  for  the  quantity  and  its  value  ;  and 
Cash,  Cr.  by  port-wine  for  the  same  value. 

As  port-wine  was  a  p:u%t  of  your  stock,  therefore  when  the  same 
sort  of  goods  are  purchased  of  several  persons  and  at  different  prices, 
it  is  convenient  to  have  some  mark  to  distinguish  them,  that  when 
the  account  of  such  goods  shall  be  balanced,  the  prime  cost  of  those, 
which  may  remain  unsold,  can  be  known. 

NOTE  4.  Buying  is  the  reverse  of.selling,  and  has  the  same  variety 
of  cases,  in  all  which  the  goods  bought  and  received  are  Dr.  but  the 
Cr.  varies  according  to  the  conditions  of  the  purchase.  The  rules  for 
buying  and  selling  merchant  goods  is  to  be  applied  in  buying  and  sel- 
ling any  thing  else  ;  a.c,  plate,  jewels,  furniture,  ship,  house,  lands,  &e. 


BY  DOUBLE  ENTRY.  239 

RULE  VII.  Goods,  bought  an  credit,  are  Dr.  to  the  sel- 
ler, and  I  he  Seller  Cr.  by  good*.  W.  and  J.  Jan.  18> 
Bought  of  A.  Newman,  linen. 

ExpL  7.  As  the  linen  is  bought,  but  not  paid  for,  you  become  Dr, 
to  A.  Newman  for  the  same  ;  but  as  you  must  not  open  an  accoun* 
-with  yourself,  and  because  the  linen  has  become  apart  of  your  stock, 
which  represents  you  the  merchant,  the  linen  must  be  made  Dr.  to 
A.  Newman,  for  the  quantity  and  its  value  ;  also  A.  Newman  Cr.  by 
linen,  for  the  same  value. 

RULE  VIIT.  Goods,  bought  for  part  cash  and  part  cred- 
it, are  Dr.  to  sundries  ;  viz.  To  Cash,  paid  in  part,  ami 
to  Seller  for  the  rest.  \V.  and  J.  Feb.  22.  Bought  of  W. 
Lamb,  broadcloth. 

P,.  Here  broadcloth  must  be  made  Dr.  to  sundries,  express- 
ing tlie  quantity  and  price  ;  and  Cash,  Cr.  by  broadcloth,  for  tin? 
money  paid  and  W.  Lamb.  Cr.  by  broadcloth  for  the  rest ;  viz.  $o75. 

RULE  IX.  When  ^oods  are  bought,  part  for  cash  and 
part  for  bill,  make  Goods  Or.  to  sundries;  viz.  To  Cash, 
for  the  sum  paid,  and  To  Bills  receivable  for  value  of  the 
bill.  W.  and  J.  April  15.  Bought  of  R.  Lakeman,  sun- 
dries. 

ExpL  9.  This  is  an  entry,  complex  in  both  its  terms,  that  is,  tws 
Drs.  and  two  Crs.  Therefore  in  this,  as  in  all  similar  cases,  the  best 
rule  is  to  resolve  the  case  into  two  entries;  viz.  First,  make  the 
Goods,  that  is,  Sundries,  Dr.  to  the  Seller,  R.  Lakeroan,  for  their  full 
value,  as  if  they  had  been  bought  on  credit ;  then  make  the  Seller, 
R.  L.  Dr.  to  sundries ;  viz.  To  Cash,  for  the  sum  paid,  and  to  Bilk 
receivable,  for  value  of  the  bill.  See  directions  for  writing  in  the 
Journal,  complex  entry. 

NOTE  5.  When  goods  are  bought,  part  for  cash,  part  credit,  and 
part  bill,  make  goods  bought  Dr.  1o  sundries  ;  viz.  To  Cash,  for  sum 
paid,  To  bills  receivable,  for  value  of  the  bill,  and  To  seller,  for  the 
rest. 

RULE  X.  When  money  is  paid,  the  Receiver  is  Dr.  to 
Cash;  and  Cash  Cr.  by  the  receiver,  for  the  sum  paid. 
W.  and  J.  Jan.  12.  Paid  James  Lewis  in  full-. 

ExpL  10.  By  the  Inventory  it  appears  you  owed  J.  Lewis  $140, 
and  consequently  he  stands  credited  by  this  sum  in  the  Leger ;  there- 
fore as  no  erasures  or  crossings  are  allowable  in  mercantile  books,  you 
must  discharge  the  debt,  by  debiting  J.  Lewis  to  Cash  for  the  money 
paid  him  in  full ;  also  Cash  Cr.  by  J.  Lewis. 

.    NOTE  6.     In  all  cases  of  paying  money  Cash,  is  Cr.  but  the  Dr. 
varies  according  to  the  terms  on  which  the  money  is  delivered. 

NOTE  7.  In  paying  money  you  mu.-l  ?.hvay~  mention  whether  in 
full  or  in  part. 


BOOK-KEEPING 

RULE  XI.  When  you  lend  money  on  security,  make  the 
JSorroiver,  Notes,  or  Bills  receivable..  Dr.  to  Cash,  naming 
the  srum  and  security ;  also  Cash  Cr.  by  the  borrower^ 
note,  or  bills  receivable,  naming  also  the  sum  and  security. 
W.  and  J.  Feb.  2.  Lent  S.  Tyler,  on  bond,  &c. 

ExpJ.  11.  You  need  only  make  S.  Tyler  Dr.  to  Cash  for  ths 
principal  received,  and  Cash  Cr.  by  S.  Tyler,  for  the  same  sum, 
emitting  the  interest,  until  it  shall  be  paid. 

NOTE  8.  When  you  borrow  money,  make  Cash  Dr.  to  the  lender^ 
notes,  or  bills  payable  ;  and  the  Lender,  Notes,  or  Bills  Payable  Cr. 
by  cash. 

RULE  XII.  When  you  pay  charges  on  goods,  repairs  or 
reimbursements  on  a  ship,  taxes  or  repairs  on  a  house,  &c.  f 
make  Goods,  Skip  or  House  Dr.  to  Cash  ;  and  Cash  Cr,  by 
3oo<ls,  ship,  house,  &c.  W.  and  J.  Feb.  20.  March  18, 
Wf.  Dec.  2. 

RULE  XIII.  When  you  pay  expenses  for  house  rent, 
servants'  wages,  or  any  other  incidental  expense  for  yourself 
or  family,  make  Expense-account  Dr.  to  Cash  for  the  to- 
tal ;  and  Cash  Cr.  by  the  same  sum.  W.  and  J.  April  6. 
Paid  expenses  this  quarter,  &e. 

ExpL  12.  A  prudent,  frugal  merchant,  while  doing' business  will 
^ver  feel  anxious  to  know  the  true  state  of  his  affairs,  and  will  there- 
i'ore  keep  a  book  of  expenses,  and  once  a  month,  or  quarter,  as  in 
ihis  treatise,  transfer  the  total  amount  to  the  Waste  book,  to  be  regu- 
'arly  posted  into  the  Journal  and  Leger,  making  Expense-account 
Or.  to  cash  fpr  the  quarterly  (or  monthly)  expenses ;  and  Cash  Cr. 
•iy  the  same. 

NOTE  9.  When  you  pay  charges  that  belong  to  trade  in  general^ 
-uch  as  warehouse-rent,  shop-rent,  postage  of  letters,  &c. ;  enter 
Charges  of  merchandise  Dr.  to  Cash. 

RULE  XIV.  AVhen  you  receive  tke  payment  of  a  debt, 
make  Cash  Dr.  to  the  payer ;  and  Payer  Cr.  by  cash  for 
the  sum  received.  W.  and  J.  Jan.  29.  Received  from 
Thomas  Lamson,  Cash  in  full. 

E.vpl.  13.  By  the  Inventory  it  appears  that  Tho.  Lamson  owed 
you  $400  ;  therefore,  to  prevent  blottings  or  crossings,  you  mast  re- 
duce'the  debt,  by  making  Cash  Dr.  to  Thomas  Lamson,  for  the  sum 
received,  and  Thomas  Lamson  Cr.  by  Cash  for  the  same  sum. 

NOTE  10.  In  all  cases  of  receiving  money  Cash  is  Dr.  but  the  Cr. 
varies  according  to  the  terms  on  which  the  money  is  received. 

NOTE  11.  In  all  receipts  for  money,  always  state  whether  in  pail 
or,  in  full. 


BY  DOUBLE  ENTRY. 

RULE  XV.  When  you  receive  interest  on  money  lent, 
or  on  notes,  make  Ca'sh  Dr.  to  Interest  account,  if  any 
opened  in  the  Leger,  if  not,  make  Cash  Dr.  to  Profit  and 
Loss;  and  Profit  and  Loss  Cr.  by  Cash.  W.  and  J.  Dee. 
30.  Received  from  Robert  Means  interest  for  9  months. 

RULE  XVI.  When  you  receive  both  principal  and  in- 
terest, make  Cash  Dr.  to  sundries;  viz.  To  Borrower  for 
the  principal,  and  to  Profit  and  Loss  for  the  interest;  also 
the  Borrower  Cr.  by  the  principal,  and  Profit  and  Loss  Cr. 
by  the  interest.  W.  and  J.  Dee.  20.  Received  from  S. 
Tyler  balance  due  on  his  bond,  &c. 

ExpL  14.  Although  you  received  all  the  balance  of  principal  and 
interest  from  S.  Tyler,  yet  you  must  make  Cash  Dr.  to  sundries,  for 
the  whole  balance  due,  and  then  make  S.  Tyler  Cr.  by  Cash  for  bal- 
ance of  the  principal,  and  Profit  and  Loss  Cr.  by  cash,  for  the  interest. 

NOTE  12.  When  notes  or  bills  receivable  are  paid  with  the  in- 
terest make  Cash  Dr.  to  Sundries,  for  the  whole  ;  and  Notes  or  Bills 
receivable  Cr.  by  Cash,  for  the  principal,  and  Profit  and  Loss  Cr- 
by  Cash,  for  the 'interest.  W.  and  J.  April  6. 

RULE  XVII.  When  you  receive  payment  in  part  or  in 
full  of  the  principal  of  money  lent,  make  Cash  Dr.  to  the 
borrower,  for  the  sum  received,  naming  the  security;  also 
the  Borrower  Cr.  by  Cash  for  the  &ame  sum.  W.  and  J. 
July  2.  S.  Tyler. 

ExpL  15.  This  case  differs  nothing  from  RuIoXIV.  rind  therefore 
needs  no  further  explanation. 

NOTE  13.  When  you  pay  cash,  for  principal  ;md  interest,  make' 
Sundries  Dr.  to  Cash,  viz.  To  the  Lender,  for  the  principal,  and  ta 
Profit  and  Loss  for  the  interest. 

NOTE  14.  If  you  pay  interest  oiihr,  make  Profit  and  Loss  Dr.  for 
the  interest. 

RULE  XVIII.  When  yo'.i  receive  the  payment  of  a 
note  or  bill,  make  Cash  Dr,  to  bills  receivable  or  to  the 
person  on  whom  the  bill  is  drawn  ;  and  Bills  receivable 
Cr.  by  Cash,  or  to  the  same  person.  W.  and  J.  Feb.  5. 
Jacob  Thomson's  note. 

ExpL  16.  Here  Cash  must  be  Dr.  to  bills  receivable,  for  J  Thom- 
son's note;  and  Bills  receivable  Or. -by  the  same. 

Let  it  be  observed,  that  if  a  note  is  dven  up  for  a  renewal  of  the 
same,  First,  make  the  person  who  dves  up  the  note  Dr.  to  bills  re- 
ceivable, and  Bills  receivable  Cr.  by  the  same  person ;  Secondly, 
Bills  receivable  Dr.  to  the  same  person,  for  the  renewed  note  or  bill; 
ai>o  ths.  Person  Cr..by  bill  or  note  renewed.  W.  and  J.  Dec.  20. 

NOTE  15.     When  you  pay  cash  for  a  bill,  note  or  acceptance  due 
from  you  to  another,  make  Bills  payable  Dr.  to  Cash,  naming  the  per- 
-on  ;  a»d  Cash  Cr.  by  bills  payable,  naming  also  the  person.     W.  and 
J.  June  10.     Aug.  25.     Oct.  30. — This  case  is  shtxil^r  to  paying- 
money  under  Rule  X. 


BOOK-KEEPING 

RULE  XIX.  When  you  give  a  bill  or  note  in  payment 
fifr  goods  purchased,  but  not  booked,  the  Person  to  whom 
the  bill  is  given  is  Dr.  to  bills  payable;  and  Bills  payable 
Cr.  by  the  same  person.  W.  and  X.  April  12. 

RULE  XX.  When  you  give  in  a  note  or  bill  to  be  dis- 
counted, make  Sundries  Dr.  to  bills  receivable;  viz. 
Cash  for  the  net  sum  received,  and  Profit  and  Loss 
Dr.  for  the  discount;  also  Rills  receivable  Cr.  by  sun- 
dries for  the  whole  value  of  bill,  W.  and  J.  Feb.  26* 
Discounted  A.  Young's  note. 

Expl.  17.  Although  you  did  not  receive  the  whole  value  of  the  note, 
it  must  be  discharged  the  same  as  if  you  did,  therefore,  Sundries  must 
be  Dr.  to  bills  receivable,  viz.  Cash  for  what  you  received,  and  Profit 
and  Loss  Dr..  for  the  discount,  and  Bills,  receivable^  Cr.  by  sundries 
for  the,  whole  face  of.  the  note. 

NOTE  16.  This,  rule  will  apply  in  all  cases  where  discount  is  made 
.'or  prompt  payment. 

NOTE  17.     When  you  discount  a  bill  to  another  person,  make  Bills 
receivable  Dr.  to  sundries  ;  viz.  to  Cash^  for.  net  sum  paid,  and  .Profit  -. 
s  Dr.  fov  the  discount. 


RULE  XXI.  When  a  person  fails,  and  compounds  with 
his  creditors,  make  the  Bankrupt  Cr.  by  Sundries,  for  the 
wliole  debt  due  by  him  ;  and  Cash  Dr.  for  the  sum  received' 
in  the  composition  ;  also  Profit  and  Loss  Dr.  for  the  Loss. 
W.  and  J,  Dec.  14.  A.  Newman  becomes  a  bankrupt,  &e. 

NOTE  18.     This  case  is  much  like  that  under  Rule  XX.  therefore 

it  needs  no  farther  explanation. 

RULE  XXII.  When  you  receive  the  freight  of  a  ship,  or 
charter  of  a  vessel,  or  the  rent  of  a  house,  make  Cash  Dr- 
to  the  ship  or  house,  for  the  sum  received,  and  Ship  or 
House  Cr-  by  Cash,  for  the  freight  or  rent.  W.  and  J. 
Nov.  27.  Received  from  Jones  &  Penniman  fre%htrof  the 
frhip  Massachusetts. 

NOTE  19.     Debit  and  credit  here  asunder  Rule  XIV. 

RULE  XXIII.  When  you  pay  cash  for  ensurance  on  a 
ship,  goods  or  cargo,  make  the  Ship  or  Goods  or  Voyage 
to  -  -,  Dr.  to  Cash,  for  the  ensurance  money  5  and  Cash 
Cr.  by  ship  or  goods  or  voyage  to  —  ,  for  the  same  sum. 
^Y.  and  J.  Feb.  23.  April  10. 

Expl.  18.  The  charge  of  ensurance  being  an  additional  expense 
on  the  ship,  goods  or  cargo,  they  must  be  debited  for  Cash  ;  and~ 
therefore  Cash  Cr.  by  ship,  goods  or  cargo,  for  the  same  sum. 


BY  DOUBLE  ENTRY. 

RULE  XXIV.  When  you  pay  money  for  charges  on  a 
voyage,  make  Voyage  to  or  from  ,  Dr.  to  Cash,  ex- 
pressing for  what ;  and  Cash  Cr.  by  voyage  to  or  from 

.     W.  and  J.  Nov.  15.     Entered  at  the  Custom-house 

my  goods  from  Bourdeaux,  and  paid  duties,  &c. 

Expl.  19*.  As  this,  like  Rule  23,  is  a  farther  expense  on  the  voy- 
age, you  must  make  Voyage  from  Bourdeaux  Dr.  to  Cash,  for  the  du- 
ties and  other  charges  ;  and  Cash  Cr.  by  voyage  from  Bourdeaux,  for 
the  same  charges. 

RULE  XXV.  When  goods  are  bartered  for  others  of 
equal  value,  make  Goods  received  Dr.  to  goods  delivered  : 
and  Goods  delivered  Cr.  by  goods  received,  naming  the 
price  and  quantity  of  each.  W.  and  J.  Jan.  20.  Bartered 
sugar  for  coffee. 

Expl.  20.  When  one  commodity  is  sold,  or  exchanged,  for  anoth- 
er, it  is  called  Barter ;  and  when  one  sort  of  goods  is  exchanged  for 
another  of  equal  value,  as  in  this  case,  make  the  Coffee  received  Dr, 
to  the  sugar  delivered. 

NOTE  20.  When  one  sort  of  goods  is  received  for  several  sorts 
delivered,  make  Goods  Dr.,  to  Sundries ;  viz.  To  the  several  sorts  of 
goods,  delivered,  for  their  respective  values. 

NOTE  21.  When  several  sorts  of  goods  are  received  for  one  sort  de- 
livered, make  Sundries  ;  viz.  the  several  goods  received,  each  for  its 
value,  Dr.  to  goods  delivered. 

RULE  XXVI.  When  several  sorts  of  goods  are  bartered 
for  several  others,  and  that  whether  the  goods,  received 
and  delivered,  are  equal  in  value  or  not,  make  two  entries; 
First — Make  the  person  with  whom  the  barter  is  made  Dr. 
to  sundries ;  thai  is,  to  each  sort  delivered,  for  its  respec- 
tive value  ;  Secondly — Make  Sundries,  that  is,  each  sort 
of  goods,  received  Dr.  to-the  person  with  whom  the  barter 
is  made,  for  its  respective  value.  W.  and  J.  April  4, 
Bartered  with  R.  Means,  &c. 

Expl.  21.  This  is  a  case  complex  in  both  its  terms,,  and  requires 
two  entries,  therefore,  First,  make  Robert  Means  Dr.  to  sundries ; 
\dz.  sugar  and  rum  delivered  him,  and  Sundries  ;  viz.  Sugar  and  Rum 
Cr.  by  the  goods  delivered — secondly,  make  Sundries  ;  viz.  Ashes  and 
Tow-cloth,  received,  Dr.  to  R.  Means,  and  Robert  Means,  Cr.  by 
sundries,  viz.  ashes  and  tow-cloth  received, 

See  directions  for  writing  in  the  Journal,  complex  entry. 

RULE  XXVII.  When  goods  are  shipped  off,  for  your 
own  account,  from  your  ware-house,  and  consigned  to  a 

factor,  make  Voyage  to ,  Dr.  to  sundries ;  viz.  To  the 

respective  goods,  for  their  prime  cost,  and  To  Cash,  for 
shipping  and  other  charges ;  also  Sundries  ?  viz.  the  re- 


BOOK-KEEPING 

spective  goods,  and  Cash,  Cr.  by  voyage  to  W.  and 

J.  May  8.  Shipped  on  hoard  the  General  Hamilton  for 
Oporto  and  consigned  to  F.  Alvardo  &  Co. 

Expl.  22.  As  the  goods  are  consigned  to  F.  Alvardo  &  Co.  for 
your  own  account,  you  must  make  voyage  to  Oporto,  consigned  to 
F.  Alvardo  Si  Co.  Dr.  to  sundries,  for  the  whole  cost  and  charges  ; 
and  the  several  articles  of  goods  shipped  (entered  in  the  books)  Cr. 
by  voyage  to  Oporto. 

NOTE  22.  Foreign  trade  comprises  three  things  ;  viz.  1.  The  ship- 
ping off  the  goods  to  a  factor.  2.  Advices  concerning  them  from  the 
factor.  3.  The  returns  made  by  the  factor  to  you. 

NOTE  23.  In  all  cases  of  shipping  off  goods  to  a  factor,  Voyage  to 
— ,  is  always  Dr.  but  the  Cr.  varies  according  as  the  goods  s'hipped 
off  are  booked,  that  is,  taken  from  your  warehouse,  or  presently 
bought,  which  may  be  either  for  cash,  or  on  credit. 

RULE  XX VIII.     When  you  ship   off  goods  bought  on 

credit,  make  Voyage  to s   Dr.  to  sundries;    viz.   To 

seller  or  sellers,  for  value  of  the  goods  at  prime  cost,  To 
Cash,  for  shipping  charges,  also  Sundries,  viz.  the  Seller 

orSellersCr.  by  the  voyage  to ,  for  the  value  of  goode, 

and  Cash  Cr.  by  the  voyage   to ,  for  the    charges. 

W.  and  J.    April  10.     Voyage  to  Bourdeanx,  &c. 

Expl.  23.  This  case  differs  but  very  little  from  the  preceding 
rule,  and  therefore  is  easily  posted,  make  the  Seller  or  Sellers  Credi- 
tors, instead  of  the  goods  as  above. 

NOTE  24.  Voyage  must  be  debited  for  all  charges  which  incref>-° 
the  cost,  and  credited  for  whatever  lessens  the  cost ;  such  as  boun- 
ties or  drawbacks  on  exported  goods  ;  thus-  for  bounties,  make  CaJi 
or  Custom-House  Debentures,  (as  you  may  receive  money,  or  pro- 
cure a  debenture-bill)  Dr.  to  voyage.  When  you  receive  paymeivt 
of  the  debenture-bill,  make  Cash  Dr.  to  Cu.stom-House  debentures. 

NOTE  25.  For  drawback?,  make  Cash,,  or  Custom-House  Bonds, 
(as  you  may  receive  cash  or  take  up  your  bond)  Dr.  to  voyage,  or 
to  goods  exported. 

RULE  XXIX.  When  intelligence,  with  the  account  of 
sales,  is  received  from  your  factors-advising  that  he  had  re- 
ceived and  sold  your  goods,  make  Factor  my  account  current 

Dr.  to  voyage  to  ,  for  the  net  proceeds,  and  that 

whether  the  goods  are  sold  for  cash,  credit,  o^part  both; 
also  make  Voyage  to ,  Cr.  by  factor  my  account  cur- 
rent, for  net  proceeds.  W.  and  J.  Nov.  8.  Received  ac- 
eount  sales  from  C.  Leroi,  of  the  net  proceeds  of  the  cargo 
consigned  to  him. 

ErpL  %4.  As  the  cargo  was  consigned  to  C.  Leroi,  for  your  ac- 
count, so  he  becomes  your  debtor,  whenever  he  advises  of  its  arrival 
and  sales ;  .therefore  you  must  make  Charles  Leroi.  my  account  cm-- 


BY  DOUBLE  ENTRY. 

rent  Dr.  to  voyage  to  Bourdeaux,  for  the  net  proceeds  ;  and  Vojage 
to  Bourdeaux  Cr.  by  C.  Leroi  my  account  current,  for  net  proceeds. 

NOTE  26.  "When  the  ship  or  goods  arrive,  make  Goods  received 
Dr.  to  voyage  from — ,  also  Voyage  from  — ,  Cr.  by  the  goods. 
W.  and  J.  Sept.  3.  Nov.  18. 

NOTE  27.  If  the  return  cargo  is-  sold  on  the  wharf  before  the  voy- 
age is  discharged  in  the  books,  make  the  Buyer,  Bills  receivable,  Cash, 
%f  the  Things  received,  Dr.  to  voyage  from  — ,  for  the  quantity  and 
value  ;  also  Voyage  from  — ,  Cr.  by  the  same,  for  the  quantity  and 
value.  W.  and  J.  Nov.  25.  Dec.  15. 

RULE  XXX.  When  your  factor  makes  a  remittance  in 
goods  to  you,  having  givpn  you  previous  notice  by  account 

sales,  or  when  the  same  arrives,  make  Voyage  from -, 

Dr.  to  factor  my  account  current,  for  cost  and  charges  of 
the  cargo,  per  invoice  ;  also  Factor  my  account  current  Cr. 
by  voyage  from  — >  for  the  same  suui.  W.  and  J.  Sept. 
3.  Nov.  12. 

NOTE  28.     A  factor  is  the  person  employed  by  the  merchant. 

RULE  XXXI.  When  your  factor,  for  goods  consigned 
to  him,  remits  to  you  a  bill,  payable  at  single  or  double 
usance,  or  any  other  time  after  date  or  sight,  upon  getting 
the  hill  accepted,  make  Bills  receivable,  stating  on  whom 
drawn,  Dr.  to  factor  my  account  current,  for  value  of 
the  bill;  also  Factor  my  account  current  Cr.  by  bills 
receivable.  W.  and  J.  Dec.  6. 

NOTE  29.  When  the  payment  of  the  bill  is  received,  make  Cash 
Dr.  to  bills  receivable  ;  and  Bills  receivable  Cr.  by  Cash.  Dec.  8. 

RULE  XXXII.  When  you  have  goods  consigned  to  you 
by  your  employer,  on  which  you  have  paid  charges,  as 
freight,  duties,  &e. ;  make  Employer  his  account  of 
goods  Dr.  to  Cash,  stating  for  what ;  and  Cash  Cr.  by  em- 
ployer's account  of  good*,  for  the  same  sum.  W.  and  J. 
March  1.  Paid  freight  on  Henry  Lee's  tobaeco. 

Expl.  25.  As  you  have  the  tobacco  in  your  own  hands,  you  need 
..nly  make  Henry  Lee's  account  of  tobacco  Dr.  to  Cash  ;  and  Cash 
Cr.  by  H.  Lee's  account  of  tobacco,  for  the  charges. 

NOTE  30,  When  there  is  but  one  kind  of  goods,  name  it  as  in  H» 
Lee's  account  of  tobacco. 

NOTE  31.  Employer  is  the  person  who  employs  the  merchant  to 
transact  business  for  him. 

NOTE  32.  Factorage  comprises  three  things,  1.  The  receiving 
of  the  employer'*  goods.  .2.  Selling  them.  3.  Returns  made  for 
tjiera.. 


BOOK-KEEPING 

RULE  XXXIII.  When  goods  consigned  to  you  by  your 
employer  are  sold  for  cash,  make  Cash  Dr  to  Employer 
his  account  of  goods,  for  the  sum  received  ;  and  employer 
his  account  of  goods  Or.  by  Cash  for  the  same  sum.  W. 
and  J.  March  14  and  24. 

Expl.  26.  As  the  Dr.  and  Cr.  applied  to  ercploj-er's  account  of 
goods  admit  the  same  varieties  as  proper  trad'e,  therefore  no  further 
explanation  is  necessary. 

NOTE  33.  When  you  sell  your  employer's  goods,  for  a  bill,  make 
Bills  receivable  Dr.  to  employer  his  account  of  goods  ;  and  Employ- 
er's account  of  goods,  specifying  the  price  and  quantity,  Cr,  by  bills 
receivable,  for  the  bill.  W.- and  J.  March  4. 

RULE  XXXIV.  When  your  emp3o\ers  goods  are  all 
sold,  balance  his  account  of  goods,  that  is,  charge  Employ- 
er's account  of  gaods  Dr.  to  Sundries;  viz,  to  Cash,  for 
any  charges  paid  by  you  and  not  yet  booked  ;  and  to  Com- 
mission account,  for  your  commission  ;  and  to  Employer  his 
account  current,  for  nel  proceeds;  also  make  Employer's 
account  current  Cr.  by  his  account  goods  for  net  proceeds, 
and  Commission  account  Cr.  by  his  account  of  goods,  for 
commission.  W.  and  J.  March  30.  Leger,  EL  Lee's  ac- 
count tobacco. 

RULE  XXXV.  When  you  remit  money  to  your  employ- 
er, make  Employer  his  account  current  Dr.  to  Cash  ;  and 
Cash  Cr.  by  employer's  account  current.  W.  and  J« 
March  31. 

RULE  XXXVI.  When  your  employer  draws  a  bill  on 
you,  payable  at  usance,  which  you  accept,  make  Employer's 
account  current  Dr.  to  bills  payable,  for  value  of  the  bill  ; 
and  Bills  payable  Cr.  by  employers  account  current,  for 
the  acceptance.  W.  and  J.  Aug.  25. 

RULE  XXXVII.  When  you  buy  up  goods  on  credit,  and 
ship  them  offby  order  for  your  employer,  make  Employer 
his  account  current  Dr.  to  sundries;  viz.  to  seller  or  sel- 
lers>  for  prime  cost  of  the  goods,  to  Cash,  for  charges,  a* 
custom,  ensuranee,  and  to  Profit  and  Loss,  for  your  commis- 
sion; also  each  particular  article  Cr.  by  employer  his  ac- 
count enrrent.  AV.  and  J.  Oct.  9.  Vender  Effingin  of 
Amsterdam,  &c. 

Expl.  27.  As  the  goods  were  shipped  for  the  account  and  risk  o 
V.  Effingin  and  not  your  own,  so  whether  they  arrive  safe  or  not,  you 
must  make  V.  Effingin  his  account  current  Dr.  to  sundries  for  the 
whole  cost;  and  each  article,  when  entered  in  the  books  as  in  this 
Case,  otherwise  the  seller,  must  be  made  Cr.  for  its  respective  value,.. 


BY  DOUBLE  ENTRY. 

RULE  XXXVIII.  When  you  buy  up  goods  for  cash  and 
ship  them  off  to  your  employer,  nvtk?  Employer's  account 
current  Dr.  to  sundries  ;  viz.  to  Cash*  for  prime  cost  and 
charges  paid,  and  to  Profit  and  Loss,  tor  your  commission. 

NOTE  34.  If  you  procure  drawback  or  bounty,  as  this  belongs  to 
your  employer,  make  Cash  Dr.  to  employer  his  account  current. 

NOTE  35.  If  you  receive  money,  bill  or  bond,  at  the  custom-house, 
by  "bounty  or  drawback,  make  Cash.  Custom-House  debentures,  or 
Custom-house  bonds,  Dr.  to  employer's  account  current. 

RULE  XXXIX.  When  good*  in  company  are  bought  on 
credit,  make  < wo  entries;  first,  make  Goods  in  Co.  (naming 
partner)  Dr.  to  the  seller,  for  the  value  of  the  goods  bought; 
and  the  Seller  Cr.  by  the  goods  bought  in  Co.  ;  secondly, 
make  each  Partner  his  account  current  Dr.  to  his  account 
in  Co.  for  his  respective  share:  also  each  Partner  his  ao- 
eount  current  Cr.  by  his  account  in  Co.  for  his  respective 
share.  W.  and  J.  Nov.  30.  Bought  of  R.  Means  pot 
ashes  in  Co.  with  D.  Whitman  and  self,  each  half. 

E.rpl  28.  As  the  ashes  is  in  Co.  you  must  first  make  ashes  in  Co. 
witft  D.  Whitman  and  self,  each  half,  Dr.  to  R.  Means,  for  the  quan- 
tity and  value ;  also  make  R.  Means  Cr.  by  ashes  in  Co.  with  D. 
Whitman  and  self,  each  half,  for  the  same  sum. 

Secondly,  As  3"ou  have  a  partner,  make  his  Account  current  Dr. 
to  his  account  in  Co  for  his  half  of  ashes  ;  also  your  Partner's  Ac- 
count in  Co.  Cr.  by  his  account  current  for  the  same  sum. 

NOTE  36.  Goods  in  Co.  or  Voyage  in  Co.  are  debited  for  all 
charges  paid  upon  them,  and  credited  for  every  article  of  profit. 

NOTE  37.  Partner's  account  current  shows  what  partner  owes  to 
the  company,  or  the  company  to  him  ;  instead  of  which  some  use 
'"  partner's  account  proper." 

NOTE  38.  When  you  receive  partner's  share  of  goods,  or  cash 
for  the  goods  bought  in  Co.  make  cash  Dr.  to  partner  his  account 
current  for  the  sum  received  ;  and  Partner's  account  current  Cr.  by 
cash,  for  the  same.  June  21.  Dec.  2. 

NOTE  39.  In  paying  for  goods  bought,  or  receiving  payment  for 
goods  sold  in  Co^  or  Voyage  in  Co.  the  entries  are  the  same  as  in 
proper  trade. 

NOTE  40.  When  you  pay  partner  his  share  of  net  proceeds,  make 
Partner's  account  in  Co  Dr.  to  cash  ;  and  cash  Cr.  by  partner's  ac- 
count in  Co  for  the  same.  Dec.  4,  5. 

NOTE  41.  After  goods  are  brought  into  partnership  there  is  no 
further  occasion  for  second  entries,  as  some  merchants  practice  ;  and 
the  entries  not  only  as  it  respects  payments,  but  in  every  other  trans- 
action will  generally,  under  similar  circumstances,  be  the  same  as  in 
proper  trade. 


BOOK-KEEPING 

RULE  XL.  When  goods  in  Co.  are  sold  for  cash,  make 
cash  Dr.  to  goods  in  Co.  (naming  partner.)  and  goods  in  Co. 
Cr.  by  cash.  W.  and  J.  Lee.  2. 

NOTE  42.     When  goods  are  bought  in  Co.  and  each  partner  pays 

his  share  in  ready  money,  or  if  he  bring  in  his  own    share  of  goods  ; 

make,  Goods  in  Co.  Dr.  to  sundries  ;  viz.     To  Cash,  or  to  Goods,  for 

your  share,  and  to  each  partner's  account  in  Co.  for  his   share. 

NOTE  43.     If  the  goods  shipped   have  been  formerly  brought  into 

Company,  make  Voyage  to ,  Dr.  to  sundries  viz. 

To  goods  in  Co.  for  their  value. 
To  Cash  ;  for  shipping  charges. 

RULE  XLL  When  goods  in  company  are  all  sold  off, 
balance  the  said  account,  that  is  charge  Goods  in  Compa- 
ny, Dr.  to  sundries  ;  viz.  to  Cash,  for  all  charges  not  yet 
booked ;  to  Commission  account,¥nr  your  commission;  to  eaclv 
partner's  account  in  Company,  for  his  share  of  gain,  and  to 
Profit  and  Loss ,  for  your  share  ;  also  make  sundries  ;  viz. 
Cash,  for  charges  not  yet  booked,  commission  account  for 
your  commission,  Partner's  account  in  Co.  for  his  share 
of  gain,  and  Profit  and  Loss,  for  your  share  of  gain,  Cr. 
by  goods  in  company.  See  Leger,  ashes  in  Co.  with  D. 
Whitman  and  Self;  also  voyage  to  Copenhagen  in  Co.  with 
S.  Dean  and  Self. 

RULE  XLII.  When  goods  are  bought  on  credit  in  Com- 
pany, and  shipped  off,  make  two  entries,  viz.  First,  make 
Voyage  in  Co.  Dr.  to  sundries,  viz.  To  seller  or  sellers, 
for  the  value  of  the  goods,  to  Cash  for  shipping  and  other 
charges  ;  also  make  ^Sellers  Cr.  by  voyage,  for  the  value 
of  goods,  and  CashCr.  by  voyage  for  charges;  Secondly, 
make  each  Partner  his  account  current  Dr.  to  his  account  in 
Co.  for  his  share  of  goods  bought  in  Co.  also  Partner's  Ac- 
count in  Co.  Cr.  by  his  account  current,  fer  his  share  of 
goods  bought  in  Co.  W.  and  J.  June  20. 

Expl.  29  Shipping  goods  in  Co.  is  so  much  like  bringing  goods  inte 
company  that  attention  to  Rule  XXXIX  and  others  respecting  "  goods 
in  Co."  will  be  sufficient  explanation  respecting  Voyage  in  Co. 

NOTE  44.  The  entries,  upon  the  advice  and  returns  of  the  factor 
are  the  same  as  in  proper  trade. 

RULE  XLI1I.  When  you  receive  the  account  sales  from 
your  factor,  or  receive  returns  of  the  goods  in  Co.  consigned 
to  him,  make  Factor  our  account  current  Dr.  to  voyage 
ia  Co.  to  i  f  for  ilie  net  proceeds  ;  also  Voyage 


BY-DOUBLE  ENTRY. 


in  Co.  to  -  (the  place)  Cr.  by  the    fuctor  our  account 
current,  for  the  same  sum.     W.  and  J.  Nov.  6. 

RULE  XLTV.  When  cash  is  remitted  by  factor,  make 
Cash  Dr.  to  factor  our  account  current;  and  Factor  our 
account  current  Cr.  by  cash  ;  for  the  same  sum.  W.  and 
J  Dec.  IS. 

RULE  XLV.  When  you  receive  a  bill  or  note  for  goods 
sold,  make  Bills  receivable.  Dr.  to  the  buyer  ;  and  the  Buy- 
er Cr.  by  bills  receivable,  for  the  same.  March  24.  De- 
cember 26. 

DIRECTIONS  FOR  WRITING  IN  THE  JOURNAL. 

1.  In  a  simple  entry,  the  Debtor  should    be  first  nam- 
ed, then  the  Creditor,  all  in   one  line  ;  after   which    the 
narration  or  cause  of  the  entry,  concisely  and  intelligibly 
expressed  in  one  line,    or  more  if  necessary.     Thus. 

Joseph  BrighamDr.  to  Port  wine, 
For  5  hhds.  at  $55  per  hhd.  $275 

Journal  Feb.  21. 

2.  In  a  complex  entry,  let  the  sundry  debtors  or  cred- 
itors be  written  in  the  first  line,  and  expressed  by  the  word 
*•  Sundries,"  with  the  sum  total  short  extended,  ail  in  one 
line,  under  which  let  each  of  the  several  Crs.  or  Drs.  with 
their  respective  sums  be  subjoined,  each  in  a  line  by  itself, 
which  being  added  must'be  carried  to  the  money  columns; 
Thus,     Broadcloth  Dr.  to  Sundries  $1750 

For  500  yds.  at  $3,50 

To  casn,  paid  in  part  $875 

—  Window  Lamb,  for  the  rest  -  875 


Journal  February  22.  1750 

Sundries  Dr  to  Richard  Lakeman  $12100. 
Fish  merchantable,  at  $3,50 — 3400  quintals         $11900 
Oil,  at  &10  per  barrel — 20  barrels  200 

Journal  April  15.  12100 

N.  B.  Every  transaction  of  the  Waste-book,  thus  en- 
tered is  called  a  "  Journal  pnst  or  entry" 

For  example,  see  J.  February  12,  "Joseph  Brigham" 
is  called  the  Dr —"  Port -wine"  is  the  6V.— -The  '  words 
"  Joseph  Brighnm  Dr.  to  Port-wine"  is  called  the  entry, 
and  the  words  whirh  follow,  the  narration. 


250 


BOOK-KEEPING 


When  two  or  more  persons  or  things  are  included  in  th« 
same  account  they  are  expressed  by  the  term  "4  Sundries," 
or  "  Sundry  accounts.'' 

A  simple  entry  is  that  which  has  only  one  Dr.  or  one 
Cr.  as  Cash  Dr.  to  rum.  Journal  January  7. 

A  complex  entry  is  either  when  one  Dr.  has  two  or 
more  Crs.  as  Broadcloth  Dr.  to  Sundries,  or  when  two  or 
«iore  Crs.  have  only  one  Dr.  as, 

Sundries  Dr.  to  Richard  Lakeman, 

•or  when  several  Drs.  have  several  Crs.  and  then  the  entry 
is  said  to  be  complex  in  both  terms.  In  such  cases  of  com- 
plex posts,  it  is  preferable  to  make  two  separate  Journal 
entries,  so  that  the  first  may  have  only  one  Cr.  and  the 
second  only  one  Dr.  This  mode  will  prevent  the  confusion 
attending  a  single  entry,  and  avoid  the  improper  ambig- 
uous, titles  of  "  Sundries  Dr.  to  Sundries." 

Bartered  with  Robert  Means  IS  cwt.  su- 
gar a  SI 2,50  per  cwt.  $225 


Waste  April  4.- 


120  gals,  rum  a  g>l,25 

For  20  casks  of  pot  Ashes 
45  2  4  Ib.  net  a  $4.94  /r 
per  cwt. 
500  yds-  tow  cloth  a 


150 


$37, 


,25 


225 
125 


350 


f  Sundries  Dr.  to  Robert  Means  $375. 
I  Ashes,  45  2  4  Ib.  net 
|  a  §4.-94-/r  $225 

I  Tow  Hoth,  500  yd«.  a  }25          125 

Journal  Entry  <(  Received  in  Barter.  ^350 

April  4.           Robert  Means  Dr.  to  Sundries  §375. 
To  sugar  18  cwt.  a  $12,25    $225 
To  rum,  120  gals,  a  SI, 25       150 
^Delivered  in  barter.  §375 

NOTE  1 .     In  complex  entries  the  sure  total  should  be  short-extend- 
ed, and  annexed  1o  the  word   u  Sundries/' 

2.  In  mentioning  the  several  Drs.  and  Crs.  the  Cr?.  have  the 
word  "  To"  written  before  them,  but  1hc  ITS-,  are  expressed  wlth- 
eut  any  word  prefixed.  £ee  preceding  Journal  entry. 


POSTING  THE 

The  first  Journal  i  r.»rv  ru, Mains    Ihe    *>i'l»sfance    of  tfee 
Inventory,  which  is  divided  into  two  parts  ;  VKS. 


BY  DOUBLE  ENTRY. 


1.  All  the  money  on  hand,  the  goods,  notes,  or  bills  re- 
ceivable, furniture,  houses,  lands,  ships,  debts  due  by  bond  or 
mortgage,  accounts,  and  every  other  kind  of  properly  which 
the  merchant  possesses.     The  difference  of  these  t\vo  parts 
shows  the  merchant's  net  stock,  or  how  much  he  is  worth 
after  all  his  debts  are  paid.     The  first  entry  i*  "  Sundries 
Dr.  to  Stock." 

The  particular  D'rs.  are,  Cash^  Goods,  Bills  receivable, 
due  to  him,  and  the  Persons  indebted   to  him. 

2.  The  second  entry  is  made,  "  Stock  Dr.  to  Sundries." 
The  particular  Crs.  are  the  Persons,  to  whom  the  mer- 

chant stands  indebted,  Rills  payable   accepted  by  him  pay- 
able to  others. 

NOTE  1.     Sbo&  is  a  term  used  to  represent  the  merchant  or  owner 
of  the  book?. 

'•2.     The  Debtors  and  Creditors  should  be  written  in  large  round 

hand,  or  text,  both  for  ornament  and  distinction  ;  and   the  figures  of 

to  the  folio,  much  smaller  than'  those  of  the  dute  or 


LEGER. 

The  Lesjer  is  the  merchant's  principal  book,  to  which 
the  several  transactions,  dispersed  through  the  Waste-book, 
hut  collected  and  prepared  by  the  Journal  entries  of  the  ti- 
tles with  the  relation  of  Dr.  and  Cr.  are  transferred  each 
to  its  proper  account. 

The  Leger  is  ruled  in  the  same  manner  as  in  single  en- 
try, with  the  exception,  that  in  this,  inner  columns  are  rul- 
ed in  accounts  of  goods,  and  a  folio  column  both  on  the 
Dr.  and  Cr.  sides,  for  references  to  the  folio,  \\here  the 
corresponding  Leger  entry  of  each  article  is  made;  for  in 
the  method  of  double  entry,  every  article  is  twice  entered 
in  the  Leger ;  viz.  on  the  Dr.  side  of  one  account,  and*Lgain 
on  the  Cr.  side  of  some  other  account,  so  that  the  figures 
have  a  mutual  reference  from  one  to  the  other,  which  also 
greatly  facilitate  the  labor  of  examining  the  accounts. 

In  posting  the  Leger,  the  following  circumstances  muit 
he  carefully  observed. 

On  the  Dr.  side  must  be  written, 

1.  The  date,  in  the  first  and  2d  left  hand  columns. 

2.  The  Journal  folio,  in  the  3d  column. 

3.  Each  creditor  title,  the  cause  of  the  entry,  in  tl« 
do. 

1.  The  transaction,  belonging  (o  the  title,  in  4th  do. 


BOOK-KEEPING 


5.  The  quantity  &c.  ^in  account  of  goods,  in  inner  col- 

6.  The  quality  &c.     £  umns,  ruled  within  the  4th  do. 

7.  The  Leger  folio  of  the  creditor,  in  the  Sth  do. 

8.  The  amount  in  dollars  and  cents,  in  the  6th  and  7th  do> 
On  the  Cr.  side  must  be  written, 

1.  The  date,  in  1st  and  2d  columns. 

2.  The  Journal  folio,  in  3d  do. 

3.  Each  debtor  title,  the  cause  of  ihe  entry,  in  the  4th  do. 

4.  The  transaction  belonging  to  the  Leger  title,    in   the 
4th  do. 

5.  The  quantity  &c.  5  in  inner  columns  ruled  in  accounts 

6.  The  quality  &c.    £  of  goods,  in  the  4th  column. 

7.  The  Leg**  folio  of  iM  Debtor,  in  the  5th  do. 

8.  The  amount  in  dol$.  and  cents,  in  6th  and  7th  do, 

NOTE.  Besides  the  seven  columns,  there  should  be  othar  inner 
columns,  ruled  between  3d  and  5th,  for  number,  weight,  measure, 
mark,  exchange  &c.  when  these  are  considered. 

In  filling  up  the  Leger,  assign  a  sufficient  space  for  each 
account,  in  the  order  hereafter  arranged,  beginning  with 
Stock9  $c. 

The  titles  of  the  accounts  are  written  over  the  account? 
with  Dr.  prefixed  on  the  left  hand  page,  and  Cr.  annexed 
on  the  right  ;  below  which  are  the  articles  with  the  word 
"  To"  prefixed  on  the  Dr.  side  and  "  By"  on  the  Cr.  side. 

Upon  the  margin  are  recorded  the  dates  of  the  articles 
in  two  small  columns  allotted  for  that  purpose,  and  one  for 
a  reference  to  the  Journal  folio. 

The  titles  are  inserted  in  the  index  under  their  initials 
with  the  folio  reference,  as  soon  as  they  are  written  in  the 
Leger. 

In  entering  the  Dr.  article,  write  on  the  line  the  name 
of  th<ypr.  with  the  word  "To"  prefixed,  giving  a  short 
liarr^ive  of  the  transaction,  and  inserting  the  quantity  and 
price,  as  directed  above. 

In  entering  the  Cr.  article,  write  the  name  of  the  Dr. 
with  the  word  "  By"  prefixed,  observing  the  circumstances 
mentioned  in  posting  the  Leger.  This  being  done  turn  to 
the  Journal,  and  in  the  folio  columns,  for  the  Dr.  and  Cr. 
of  the  account,  insert  the  figures,  which  refer  to  the  Dr. 
and  Cr.  of  the  account  just  posted.  Thus  proceed  till  all 
the  Journal  is  transferred  to  the  Leger. 

The  accounts  in  the  Leger  should  be  arranged  accord. 
ing  to  their  importance.  The  common  order  is  the  same, 
ia  which  they  stand  in  the  Journal.  This,  however,  is  not 


BY  DOUBLE  ENTRY. 

filial,  but  is  the  most  regular  method,  and  the  most  con- 
venient for  scholars. 

The  following  is  the  arrangement  adopted  in  this  treatise, 

1.  Stock,  7.  Personal  accounts. 

2.  Cash,  8.  Commission, 

3.  Bills  leeeivable,  9.  Expense  account, 

4.  Bills  payable,  10.  Voyages  to  and  from, 

5.  Profit  and  Loss,  To*  which  may  be  added 

6.  Houses,  lands,  ships,        Balance,  and  Interest  ae- 
ancl  other  possessions,       count. 

The   preceding   accounts   may   be   distinguished  under 
three  general  kinds,  viz. 
I.  lieaL  which  in  the  Leger  is  particularised  by  the  titles, 

1.  Cash,  i.  e.  all  the  ready  money. 

2.  Goods  general  and  particular  ;  in    my  own  hands   for 

my  own  account. 

3.  Voyage  to  ;  when  consigned  to  another  for  my  accountv 
4    Such  a  person  his  account  of  goods  ;  when  in  my  owe 

hands  for  another's  account. 

5.  Guod*  in  Co.  with ;  when  under  my  direction  for 

self  and  others. 

6.  Bills  receivable  :  when  the  bills  are  payable  to    me. 

7.  Bills  payable  ;  my  own  bills  or  notes  payable  to  others, 

8.  House  or  land  in  such  a  place;  for  Houses  and  Lauds;, 

9.  Ship  such  a  one  ;  for  ships. 

NOTE.  Such  a  person  his.  account  of  goods  ;  his  account-current,  aiicl 
his  account  on  time,  are  u^ed  by  the  Factor,  or  person  employed  by 
tffe  merchant  ;  also  such  a  person  my  account  of  goods  ;  my  (or  our) 
account  current,  and  my  account  on  linn,  are  uf-.ed  by  the  employer,. 
or  person  who  employs  the  merchant. 

II.  Personal;  accounts  with  persons. 

Title  1.  Stick  a  person  (naming  him);  for   a  common  per- 
sonal account. 

2.  Such  a  person  his  account  /  an    account  current  of* 

another  person's  atrV.irs  transacted  by  me. 

3.  Such  a  person  my  account  ;  an  account  current  of 

my  aff-iirs  done  by  another  person. 

4.  Such  a  person  his  account  in  Co.  ;   an   account  of 

the  share  a  partner  has  in  Co.  under  iny  direction, 

III.  Fictitious   or  Imaginary  ;    that   is  accounts  repre- 
senting the  Merchant  himself,  or  the  owner  of'  the  Books. 
Title  1.  Slock ;ilmt  is,  the  Merchant. 

2,  Profit  and  Loss  :  the  general  account  of  the 
ehaut's  gains  aud  losses, 


BOOK-KEEPING 

3.  Commission  ;  the  particular  charges  the  merchant 

has  made  as  factor  for  another. 

4.  Expense  Account;  the  particularcharges  he  has  been 

at  in  the  course  of  his  business,  house  expenses,  &e. 

5.  Interest  ;  the  gain  or  loss  the    merchant  has  made 

by    interest.     This  account  may  as  well   be  kept 
with  that  of  Profit  and  Loss. 

RULES  FOR  DEBITING,  CREDITING  AND  BAL- 
ANCING ACCOUNTS  IN  THE  LEGER. 

t.  Cash  in  debited  for  all  the  money  on  hand,  at  the 
commencement  of  business,  also  for  all  sums  received  af- 
terwards. It  is  credited  for  all  money  paid  out,  and,  at 
closing  the  books,  is  credited  "  By  balance/'  for  the  excess 
of  the  debit  above  the  credit ;  which  is  the  amount  of  the- 
money  on  hand.  See  Leger,  Cash,  page  2. 

If  the  money  remaining  on  hand  should  not  agree  with  this  sum, 
an  error  exists  in  the  account,  which  must  be  sought  after  and  cor- 
rected. 

2.  Goods.  The  accounts  of  goods  have  inner  columns 
for  the  quantities,  &c.  :  See  Leger,  Broadcloth,  Linen,  &c. 

At  opening  the  books  all  the  goods  on  hand  as  by  the 
inventory,  also  those  purchased  afterwards,  are  enlered  on 
the  Dr.  side  of  their  respective  accounts  ;  and  goods  sold, 
on  the  Cr.  side,  with  the  quantities  of  both  entered  in  the 
inner  columns,  and  their  values  in  the  outer. 

All  money  expended  on  goods  is  debited,  and  all  advantages  aris*- 
^ng  from  them  are  credited. 

.If  no  part  of  the  goods  are  sold,  credit  the  account  "  By  balance," 
for  the  whole  sum  on  the  Dr.  side. 

If  the  sums  in  the  inner  columns  on  the  Dr.  and  Cr.  sides  are 
equal,  the  goods  are  all  sold,  and  then  the  balance  of  the  money  col- 
umns will  exhibit  the  gain  or  loss  ;  therefore  debit  the  account'1'  To 
Profit  and  Loss,"  for  the  gain,  or  credit  it  "  By  Profit  and  Loss,"  for 
the  loss. 

If  the  credit  exceeds  the  debit,  it  is  gain ;  if  the  debit  is  the  great- 
er, it  is  loss. 

If  the  sum  of  the  inner  column  on  the  Dr.  side  is  the  greater,  part 
of  the  goods  remain  unsold  ;••  their  value  at  the  prime  cost  must  be 
added  to  the  sum  on  the  credit  side  to  ascertain  the  gain  or  loss. 
First,  credit  the  account  "  By  balance,"  for  what  remains  unsold  ; 
Secondly,  close  the  account,  afterwards,  with  "Profit  and  Loss," -for 
the  gain  or  loss. 

The  merchant  may,  at  any  time,  know  what  goods  he  has  on  hand 
•without  the  laborious  task  oY  taking  an  account  of  stock,  that  is,  by 
vrrifrirn:- or  rrpasrviivr  HIP  proorls,  by  comparing  the  inner  columns 


BY  DOUBLE  ENTR'f, 

&.  Voyage  to  or  from  ;  This  account  is  debited  for  the 
prime  cost  and  charges  of  the  cargo,  and  credited  "  by  fac- 
tor my  account  current,"  or  the  amount  of  net  proceeds,, 
ascertained  by  (he  account  sales  received  from  the  factor, 
or  by  the  returns  made  by  him.  See  Leger  ;  Voyage  to 
Bourdeaux.  p.  10. 

If  the  account  of  sales  is  not  received,  ^credit  ths  account  u  By 
balance"  for  the  total  of  the  Dr.  side. 

If  the  account  of  sales  is  received,  the  account  is  credited  uBy 
the  factor,  ray  account  current."  and  the  account  is  closed  u  By 
Profit  and  Loss,"  for  the  difference  between  the  Dr.  and  Cr.  sides, 
See  Leger,  Voyage  from  Oporto,  p.  12. 

If  goods  or   bills  are  received  in  return  for  the  net  proceeds,    the 
account  of  voyage  from is  credited  "  By  the  amount  of  said  re- 
turn," and  is  closed    u  By  Profit  and   Loss."     See   Leger,    Voyage - 
irom  Bourdeaux.  p.  11. 

4.  Such  a  person,  his  account  of  goods  ;  This  account  is 
debited  for  all  the  charges  on  (he  goods,  paid  by  you  (the 
factor)  ;   and  credited  by  the  sales  made  of  them. 

If  the  sales  are  finished,  and  no  account  kept  on  time,  debit  em- 
ployer his  account  of  goods  to  sundries;  viz. -to  cash,  for  charges  &C. 
to  commission,  for  your  commission  ;  to  employer  his  ac count  current, 
for  the  net  proceeds,  which  is  ascertained  by  subtracting  all  the  char- 
ges from  the  amount  of  sales.  See  Leger,  Henry  Lee's  account  of 
tobacco,  p.  8. 

If  the  sales  are  not  finished,  close  the.  account  by  a  double  balance^, 
when  the  account  is  kept  in  the  Leger. 

5.  Goods  in  Company;  The  Dr.   side   of  this   account 
contains  the  prime  cost,  with  all  the  charges  and  your  com- 
mission ;  the  Cr.  side  all  the  sales,  or  disposal  of  the  goods. 
The  difference  between  the  Dr.  and  Cr.  sides   is   the  gain 
or  loss,  which  is  to  be  divided  among  partners. 

If  the  sales  are  finished,  the,  account  is  closed  with  each  partner* 
liis  account  in  Co.  for  his  share  of  net  gain,  and  Profit  and  Loss,  for 
your  share.  See  Leger,  Ashes  in  Co.  with  D.  "Whitman,  p.  12.. 

NOTE,  Voyage  in  Co.  or  ship  in  Co.  are  in  their  nature  similar 
fo  goods  in  Co.  and  are  closed  in  the  same  manner.  See  Leger, 
Voyage  to  Copenhagen  in  Co.  with  S.  Dean.  p.  10. 

6.  Bills  receivable  /This  account    contains,  on  the  Dr. 
side,  the  bills  payable  to  the  merchant ;  the  Cr.   side  con- 
tains the  pnymeuts  he  has  received,  or  the  disposal  of  the 
bills  in  payment.     The  account   is  closed  by    "Balance,'9 
for  the  bills  remaining  unpaid.     See  Leger,  Bills  receiv- 
able, p.  4?. 

7.  Bills  payable,  or  notes,  drafts  accepted  by  the  mer- 
chant,  payable  to  others,   are  credited  and    the    payments 


256 

he  has  made  are  debited.  The  account  is  closed  "  By  bal 
ance,"  for  those  which  are  unpaid.  Bee  Leger,  Bills  pay- 
able, p.  2. 

8.  Houses,  Lands  and  Ships;  These  accounts  are  debited 
for  their  prime  cost,  or  with  all  charges,  as  taxes,  repairs 
&c.  ;  and  credited  for  the  profits,  as  rents,  freight  Sec.  re- 
ceived. 

If  the  bouses,  lands  &c.  are  sold  in -whole,  or  in  part,  the  amount 
of  sales  is  credited.  The  balance,  after  valuing-  at  prime  cost  what 
remains  unsold,  exclusive  of  charges,  shows  the  gain  or  loss.  The 
account  is  closed  "  By  Profit  and  Loss,"  for  the  remaining  difference. 

If  any  property  remain-!  on  hand  at  the  th^  of  balancing  the  ac- 
count, the  value  of  it,  at  prime  cost,  is  credited,  and  in  such  case, 
the  balance  shows  the  gain  or  loss,  as  the  Dr.  or  Cr.  side  is  the 
greater. 

9.  Personal  accounts  ;  The  Dr.  side  contains   the  char- 
ges against  the  merchant,  the  Cr.  his  charges  against  oth- 
ers.    These  accounts   are    debited   and   credited   as    they 
stand  Dr.  and  Cr.  in  the  Journal.     If  the  Dr.  side   is   less 
than  the  Cr.  the-  difference  is  a  debt  due  by  the  merchant, 
therefore,  debit  the  account 4i  To  balance  due  to  him  5"   if 
the  Cr.  side  is  less  than  the  Dr.    the  difference    is   a  debt 
due  by  him  to  the  merchant,  therefore,   Cr.    the   account 
"  By  balance,  due  to  me." 

If  both  sides  are  alike,  the  account  closes  itself.  See 
Leger,  Personal  accounts." 

10.  Such  a  person  his  account  current  ;  the  Dr.  side  con- 
tains your  charges  against  your.employer  with  all  the  ex- 
penses paid  on  his   account;  the   Cr.   side    contains   what 
you  (being  his  factor)  have  received  fur  his   account.     See 
Leger,  Lee's  account  current,  p.  8. 

When  you  balance  the  Leger  without  settling  with  your  employ- 
er or  furnishing  him  with  his  account  current,  close  the  account  with 
balance,  or  a  double  balance,  without  entering  your  commission^, 
'interest,  postage,  Sec. 

If  the  Cr.  side  is  the  greater,  the  difference  i?  a  debt  due  to  your 
employer  ;  if  the  Dr.  side  is  the  greater,  the  difference  is  a  debt  due- 
by  the  employer  to  you. 

When  you 'forward  employer's  account  current,  and  settle  with 
him,  clebit.his  account  to  commission  account,  for  your  commission  ; 
to  cash,  for  charges,  &c.  and  then  close  the  account  with  u  Balance.*** 

Bee  the  form  of  an  account  current  to  be  sent  to  your  employer, 
without  the  corresponding  Drs.  and  Crs.  of  the  Leger  account,  N.  VIL 

11.  Such  a  person  my  account  current ;  The  Dr.  side 
contains  your  charges  against  the  factor,  or  what  he  has- 
received  for  yonr  account,,  or  the  remittances  you  have 


BY  DOUBLE  ENTRY, 

made  to  him;  the  Cr.  side  contains  what  he  lias  paid  for 
your  account,  and  the  disposal  of  your  goods,  and  his  re- 
mittances to  you. 

If  the  Dr.*  side  is  the  greater  the  difference  is  a  debt  due  by  the 
factor  to  the  merchant;  if  the  Cr.  side  is  the  greater,  the  difference 
is  a  debt  due  by  the  merchant  to  the  factor. 

If  the  two  sides  of  this  account  are  equal,  the  debt?  between  you 
and  your  factor  are  cleared,  and  the  account  closes  itself. 

12  Such  a  person  his  account  in  Co.  Partner's  account 
in  Co.  contains  on  the  Cr.  side  partner's  share  of  the  capi- 
tal, with  hit  share  of  gain  at  the  close  of  sales,  the  Dr. 
side  contains  partner9!*  share  of  net  proceeds,  with  his 
•hare  ofb**,  if  any,  See  Leger,  D.  Whitman,  hit)  account 
in  Co,  p.  12, 

If  returns  are  fully  made  this  account  closes  it»elf  ;  but  if  no  re- 
turns  are  made  or  made,  in  part  only,  it  is  closed  with  u  balance." 
This  account  may  be  closed  with  partner's  account  current,  if  that, 
at  closing  the  Leger,  has  its  sides  unequal. 

13.  Stock  account ;  This  account  contains  on   the    Dr. 
side,  the  amount  of  debts  due  by  the  merchant,   according 
lo  his  Inventory  when   he  commenced    business  ;  the    Cr. 
side  contains  the  amount  of  ready  money,  goods,  debts  &c, 
belonging  to  him  at  that  time. 

The  balance  shows  what  his  net  stock  is  at  the  com- 
meneement  of  business ;  or  in  case  of  bankruptcy  how  much 
he  is  deficient. 

Nothing  more  is  entered  on  this  account,  till  the  closing 
of  the  books,  when  the  "  balance'*  of  the  Profit  and  Loss 
account  is  transferred  lo  it,  crediting  the  profit  and  debit- 
jog  the  loss. 

The  difference  between  the  debit  and  credit  shows  th& 
merchant's  net  stock  at  the  time  of  closing  the  books,  when 
it  is  made  Dr.  "  To .  Balance."  See  Leger,  Stock,  p.  1. 

14.  Profit  and  Loss  ;  This  account  is  credited  for  every 
article  of  gain  upon  bargains   or  goods,  during  the    course 
of  trade  ;  and  is  debited  for  every    article,   delivered    for 
which  nothing  is  expected  to  be  received  as  an  equivalent  5 
•also  for  all  losses  on  bargains  or  goods. 

The  balance  will  exhibit  the  net  gain  or  loss,  since  the 
commencement  ofbusiness ;  and  is  closed  "To  or  By  Stock." 
See  L^ger,  Profit  and  Loss  account,  p.  3. 

15.  Commission  ;    This  account  is  credited  for  all  gains 
which  the  merch-inf  has  by  commission  on  buying  and  sell- 
ing goods  for  others  ;  the  Dr.  side   is    commonly   empty, 


ttOOK-KEEEIXG. 


The  account  is  closed  by  "  Profit  ^nd  Loss."     See  Leger, 
Commission  account.  p.  9. 

16.  Expense  account  ;  Tiiis  account  is    debited   for  all 
charges  (he  merchant  has  paid  for  men's  wages,  Sec.,    and 
is  closed  by  '•  Profit  and  Loss"  for  the  difference  of  the  Dr. 
and  Cr.  sides.     See  Leger.  expense  account,  p.  10. 

17.  Interest;  This  account  is  debited  for  sums  the  mer- 
chant pays  for  interest,  and  credited   for  what  interest  he 
has  received.     It  is  closed  by  being  debited  to,  or  credited 
by  "  Profit  and  Loss,"  for  the  difference  of  the  Dr.  and 
Cr.  sides. 

18.  Balance  $  This  account  is  debited  for  all  that  is  due 
to  the  merchant,  and  credited  for   all  that  is  due    by    him 
toothers.     The  difference  between    the    Dr.  and  Cr".  sides 
is  the  merchant's  net  slock  or  estate,  at  closing  the  books  5. 
and,  consequently,  the  entry  brought  from  4i  Stock  account  " 
will  make  the  sides  of  the  Balm;  -inal,  that  is, 
it  is  closed  "  By  stock,"  brought  to  it.  See  p.  12. 

OFPOLVTIJVQ.  AMD  CORRECTING  THE  LEGER. 

Before  the  Leger  can  be  balanced  the  several  books 
must  be  perfectly  correct.  Two  methods  may  be  used  to. 
ascertain  their  correctness  ;  viz.  by  pointing  the  books,  or 
by  forming  a  monthly  or  general  trial  balance.  The  Book- 
keeper may  make  use  of  such  marks  in  pointing  as  may  be 
most  convenient,  which,  however,  shouid  be  done  with  a 
lead  pencil,  that  they  may  be  rubbed  out  when  all  the  cor- 
rections are  completed.. 

First.  Compare  the  Journal  with  the  Waste-book,  and 
see  if  every  article  is  -correctly  posted  and  the  sums  cast 
up  right.  Correct  each  mistake  as  you  proceed,  making 
the  correction  on  the  article  itself,  if  possible  ;  otherwise 
there  refer  it  to  the  nest  convenient  place,  where  the  arti- 
cle must  be  entered  anew  and  the  mistake  mentioned, 

If  no  mistake  is  found  in  the  article,  or  when  you  have 
corrected  one,  make  a  mark  on  the  left-hand  margin  di- 
rectly against  the  article,  denoting  that  it  is  examined  and 
poste'd  into  the  Journal  correctly.  Proceed  in  the  same 
manner  through  the  Waste  and  Journal. 

Proceed  in  the  same  manner  to  compare  the  Journal 
and  Leger,  but  with  greater  care,  as  the  Leger  is  more 
liable  to  mistakes,  which  may  arise  from  the  following 
Causes,  viz. 

i.  The  article  may  have  been  wholly  omitted, 


BY  DOUBLE  ENTRY,  250 

2.  It  may  have  been  twice  posted. 

3.  \  wrong  *eeourn  may  have  been  debited  or  credited. 
4-  A  debit  or  a  credit  may  have  been  omitted. 

5.  The  Dr.  may  have  been  carried  to  the  Cr.  or  the  Cr, 
to  l he  Dr.  side. 

6.  An  article  may  have  been  carried  to  two  Drs.   or  to 
iwo  Crs.  side?. 

7.  The  sum  may  have  been  added  or  carried  nut  wrong. 
A  mistake   arising  from   any  of"  tJ;e   preceding   causes 

must  be  carefully  corrected  before  a  balance  of  the  books 
«an  be  made. 

If  an  article  is  found  to  be  correct,  set  a  mark  in  the 
Leger,  at  the  right-hand  of  th?  sum,  and  another  in  the 
Journal  at  the  left-hand  of  the  folin  column  of  Dr.  t&nd  Cr. 
denoting,  that  the  article  is  examined  and  found  to  be  cor- 
rect. 

To  preserve  neatness  in  the  books,  and  to  avoid  any  al- 
teration which  may  have  the  appearance  of  a  i'r.tiidiilent 
intention,  yon  must  neither  erase,  nor  cross  any  Article  in 
correcting  mistakes.  If  any  article  is  omitted,  supply  it 
by  a  proper  entry,  adding  the  word  "  omitted." 

If  the  entry  was  made  on  a  wrong  title,  or  account,  put 
it  in  its  proper  place,  and  set  the  sum  <m  the  contrary  side 
of  the  wrong  account,  saying,  i%  To*'  or  •'  B\  error,"  on 
the  article  of  such  a  date  on  the  other  side 

If  the  sum  carried  out  is  less  than  it  should  be,  debit  or 
credit  the  account  on  the  same  side  ;  saying, "  To  or  By5' 
the  same  Dr.  or  Cr.  for  the  difference,  naming  the  month, 
date,  and  referring  to  the  folio  column. 

If  the  sum  set  down  is  greater  than  it  should  be,  place 
the  excess  on  the  contrary  side  ;  saying,  *•  To  or  By  error,'* 
an  such  au  article  ou  the  other  side. 

TRIM  BALANCE. 

The  sum  total  of  the  Dr.  side  of  the  Leger,  must  be  pqnal 
to  that  of  the  Cr.  To  prove  this,  form  a  "  Trial  Balance" 
See  the  form  annexed  to  the  Leger. 

Insert  in  the  first  and  second  columns  of  tin*  trial  Kal- 
ance  the  sum  total  of  each  account  in  the  Legcr.  rX;-<  »»t 
those  accounts  which  close  themselves.  Subtract  ihe.'  -s 
side  from  the  greater  of  each  account,  and  set  the  »'!!;. -r- 
cnc->  in  the  third  or  fourth  columns  of  the  trial  h*. !«••.•  e, 
as  i«  may  properly  belong,  a?id  at  the  same  t.mt  inserting 
\\i\\\  peiicii  mark,  the  difference  ou  ihe  less  side  of  the  ae- 


260  BOOK-KEEPING 

count  in  the  Leger  ;  which  being  added  will  balance,  that 
is,  will  make  both  sides  equal,  at  closing  the  books. 

Add  up  the  third  and  fourth  columns  of  the  trial  bal- 
ance, and  if  the  sums  agree,  the  Leger  is  proved  to  be  cor- 
rect ;  otherwise  the  books  cannot  be  brought  to  a  balance, 
till  the  error  is  corrected. 

The  correctness  of  the  Leger  being  thus  proved,  the  clos- 
ing of  if  remains  to  be  done,  which  may  be  thus  performed. 

1.  Form  a  Profit  and  Loss  sheet,  like  the  oue   annexed 
to  the  Leger. 

2.  Take  from  the  Leger.  or  the  trial  balance,  all  the  ac- 
counts which  «*lo*e    with  Profit  and  Loss,  and    enter   the 
halanee  of  each  on  its   respective    Dr.  and   Cr.  side  of  the 
•Profit  and  Loss  sheet  ;  and  to  the  Profit  and  Loss  sheet  add 
the  debits  and  credits  of  the  Profit  and  Loss  account 

3.  Add   up  both  sides   and  subtract   the    less  from  the 
greater,  the  balance  will  exhibit  the   gain,  which  must  be 
debited  if  the  Cr.  side  be  the  greater,  '•  To  stock  for  net 
gain,"  and  will  balance  both  sides  of  the  Profit  and   Loss 
sheet,  in  case  no  error  is  committed. 

Transcribe  the  Profit  and  Loss  sheet  .into  the  Waste 
hook,  and  from  that,  by  the  usual  method  into  the  Journal 
and  Leger. 

The  next  thing  to  be  done  is  to  make  a  "  Balance  (LC- 
count,"  similar  in  form  to  the  one  following  the  Profit  and 
Loss  sheet. 

Take  from  the  Leger,  or  trial  balance,  all  the  accounts 
which  close  with  "  Balance,"  except  that  of  Stock,  which 
will  be  taken  from  the  Dr.  side  of  that  account  in  the  Le- 
ger when  the  sides  of  the  balance  sheet  are  to  be  added 
up ;  and  must  be  carried  to  the  Cr.  side  of  the  balance 
sheet.  This  will  make  both  sides  equal,  if  there  is  110 
error. 

The  next  thing  to  be  done  is  to  transfer  the  "  Balance 
sheet''  to  the  Journal,  by  making  '»  Balance  account  Dr.  to 
Sundries,"  taking  the  particulars  from  the  Dr.  of  the  Bal- 
ance sheet ;  also  by  making  *'  Sundries  Drs.  to  Balance  ac- 
count." taking  the  particulars  from  theCr.  side 'of  the  Bal- 
ance sheet,  including  the  stock  account.  See  J.  p.  13. 

Each  balance  must  then  be  transferred  to  its  proper  ac- 
count in  the  Lesjer,  inserting  in  the  column  of  the  Journal 
the  number  of  reference  to  the  folio  in  the  Leger. 


BY  DOUBLE  ENTRY. 


OF  CLOSING  THE  ACCOUNTS  IJV  THE  LEGER. 

Having  added  up  the  money  columns  on  the  Dr.  and  Or. 
sides  as  before  directed,  make  both  sides  equal  by  adding 
the  difference  of  the  two  sides  to  the  less  ;  and  thus  pro- 
ceed with  cash  account  in  the  Leger,  and  the  accounts 
will  be  closed. 

In  forming  a  new  set  of  Books,  make  out  an  inventory  in 
the  Waste-book  from  the  balance  account  of  the  Leger.  The 
entries  in  the  new  Journal  will  be  "  Sundries  Dr.  to  Stock  /' 
the  particular  debtors  being  taken  from  the  Dr.  side  of  the 
"  balance  account."  Also,  "  Stock  Dr.  to  Sundries  /'  the 
particular  creditors  being  taken  from  the  Cr.  side  of  the 
"  balance  account." 

Thus  by  the  Balance  of  the  Leger  will  be  found,  1.  What 
stock  there  is  to  begin  another  set  of  books.  2.  What  the 
gain  or  loss  has  been  since  the  commencement  of  trade  ; 
and  from  the  balance  sheet,  which  is  an  account  formed 
with  the  Dr.  and  Cr.  the  stock  is  ascertained.  The  gains 
and  losses  are  found  in  the  account  of  Profit  and  Loss  ; 
the  several  articles  transferred  into  the  accounts  of  "Stock'' 
and  "  Profit  and  Loss,"  are  found  by  balancing  or  closing 
every  account  in  the  Leger. 

Some  accounts  balance  of  themselves  ;  some  are  closed 
with  "  balance"  only,  others  with  "  Profit  and  Loss"  only  ; 
Balance,  also  Profit  and  Loss  are  closed  with  "Stock  ;" 
and  Stock  balances  of  itself,  in  case  no  errors  are  commit- 
ted, which  is  the  best  proof  of  the  correctness  of  the  books. 


WASTE-BOOK. 


Boston,  January  1,  1817. 


J.  F. 
1 


Inventory  of  the  estate  of  Thomas  Russell, 
merchant. 

Ready  money,  deposited  in  the  Union  Bank  $4000 
House  in  Hanover-street,  value  -  2500 

Land  in  the  county  of  Washington,  in  the 

Province  of  Maine,  750  acres,  a  ,75     -          562,50 
Ship  Massachusetts,  value      -  7000 

Household  furniture 1500 

Jacob  Thomson's  note,  dated  Nov.  10  last, 

payable  to  my  order,  at  6  months     $350 
David  Jones'  note,  dated  Dec.  3,  last, 

payable  to  my  order,  at  3  months       410 

760 

Broadcloth,  250  yds.  a  $3,50  per  yd.     -     -     875 

Linen,  400  yds.  a  ,80 320 

Port-wine,  7  hhds.  a  $45  per  hhd.  -  -  -  315 
Sugar,  20  hhds.w'g.  240  cwt.  a  $10,50  pr.  cwt.  2520 
Rum,  12  puncheons,  a  $125  per  pun.  -  1500 
Thomas  Lamson,  merchant,  Boston,  owes  me  400 
Amos  Locke,  carpenter,  Salem,  owes  me  275 


1  List  of  debts    and  notes   owed  by   the  sak 
Thomas  Russell. 

To  James  LeAvis,  merchant,  Boston,     -          $140 
L.  Samson,  mer.  Boston,  payable  on  denVd.  800 
James  Munson,  merchant,  Boston,  pay- 
able on  demand         -  2050 
Joseph  Franklin,  merchant,  Boston,  pay- 
able on  demand,      ....          "-       1500 


1  Sold  Charles  Lee,  at  5  months.  72  cwt.  sugar 

a  g!2,50  per  cwt.         - 
i  Rule  I. 

| , 7 . 

1  Sold  for  cash, 9  puncheons  rum, a  $135perpuu 


Rule  II. 


12 


Paid  James  Lewis,  in  full 

Rule  X. 
15  _ 


1  Bo'tfor  eash,  8  hhds.  port- wine, ';  §42  pr.  hhc 

Rule  VI. 

i 18 


1  Bouebt  of  Andrew  Newman,  1000  yds.  linen 
i      «,70 
!Rule  VI 


a  ,70  per  yd. 


2252^ 


4490 


900 
1215 

14ot 
336 


i 

7001 


\\ASTE-BOOK. 

Boston,  January  19?  1817 


263 


Bought  for  cash,  84  c\vt.  sugar,  a  gl 0,72.6^ 
per  cwt.         ------- 

Rule  VI. 

20 


Bartered  84  cvvt.  sugar,  a  $12  per  cut.  lor 

4032  lb.  coffee,  a  ,25  per  Jb. 
Rule  XXV. 


Paid  Joseph  Franklin,  in  full 

Rule  X. 


Paid  James  Mtinson,  in  full 
Ride  X. 


901 

1003 
1500 

2050 


Sold  A.  Eastman  my  750  acres  of  land, 

acre,  in  payment  of  which  I  have  receiv- 
ed cash,  in  [  -  -         $350 
And  his  bill,  at  11  months,  with  interest, 
for  balance         ._--__        475 
Rule  IV. 


23 


Paid  Lemuel  Samson,  in  full 
Rule  X. 

29 


Received  from  Thomas  Lamson,  in  full 
Rule  XIV. 

31 


Received  from  Amos  Locke,  in  full 
Rule  XIV. 

February  2 


Lent  Samuel  Tvler,  on  bond,  at  (3  per  cent. 
Rule  XI. 

5 


Rec'd  from  J.  Thomson,  payment  of  his  note 
Rule  XVIII. 

1 0 


Sold  for  cash  400  yds.  linen,  a  $1,10  per  yd. 
Rule  II. 

12 


Sold   J.   Brieham,  5  lilids.  port-wine,  a  $55 

perLhd.         -         -'       -         -         - 
Rule  I. 

15 


Bo't  for  cash,  220  bhls.  of  Hour,  a  £8,75  pr.  bbl. 
Rule  VI. 


825 
800 

400 

275 

2000  i 

350  j 

440 : 

275 : 
1925 


WASTE-BOOK. 


Boston,  February  18,  1817. 


B't  of  D. Whitman,  1250  Ib.  hyson  tea,  a  $  1,25 

Rule  VII. 
20 


Paid  W.  Hart,  for  repairs  on  the  ship  Mass. 

Rule  XII. 

22 


Bo't  of  W.  Lamb  500  yds.  broadcloth,  a  §3,50 
For  which  I  paid  cash  in  part         .       .        $875 
Balance  due  him  is         ....       875 

Rule  VIII. 


Sold  to  Nye  Freeman  GOO  yds.  linen,  a  gl,20 
for  which  he  has  given  roe  a  bill  on  A.  Young,  paj-- 
able  in  3  months  ..... 

Rule  V. 

26 


Discounted  with  the  Massachusetts  Bank,  A. 

Young's  note,  at  3  months         .          .         $720 

discount     .     .      11,16 

Net  sum  received         ....         

Rule  XX.     See  Pract.  Arith.  p.  153.     Bank  Dis. 

28 


Effected  Ensu ranee,  at  the  Union  Ensu  ranee 

Office,  on  the  Massachusetts  from  Boston  to  London 
and  from  thence  to  Boston,  $6000  at  3£  per  cent 
premium  .  .  .  .  .  $210 

Policy         .         .         ,75 

Rule  XXIII.  See  Pract.  Arith.  p.  148.  

March  1 


Henry  Lee  of  Norfolk,  Vir.  has  consigned  lo 

me  by  the  brig  Favorite,  Cupt.  C.  Hunt,  15  hhds. 

tobacco,  for  sale  on  his  account ;  on  which  1  have 

paid  freight  a  §2,75  per  hhd. 
Rule  XXXII. 
4 


Sold  W.  Paterson,per  bill  payable  in  5  months. 

4  hhds.  of  Henry  Lee's  tobacco,  weighing  as  fol- 
lows; viz.     No.  1.    10  3  14lb.      tare  145  Ib. 

2.  11  2  16  150 

3.  9  3  24  135 

4.  10  0  27  140 

42  2  25  Ib.  570  Ib. 

is  4215  Ib.  net,  «  $6,80  per  100  Ib. 
Rule  XXXIII.  N.  33.     See  Pract.  Arith.  p.  110. 

_ 7 


Sold  for  cash  100  bbls.  flour,  a 

Rule  II. 


WASTE-BOOK 


Boston,  March  10, 1817- 


J.  F. 


3  Paul  truckage,  on  H.  Lee's  tobacco,  15  hhds. 

a  ,75  per  hhd. 
Rule  XXXII. 

14 


3  Sold  for  cash  8  hhds.  of  H.Lee's  tobacco,  w'g. 
as  follows  ;  viz.  No.  5.    8  2  13  Ib.  gross,  tare  135  Ib. 

6.  9  1  140 

7.  10  0  14  138 

8.  8  3  15  145 

9.  7  3  23  125 
10.    9  1  13  132 
11.10  0  14  140 
12.    8  2  14                         130 

72  3  22  Ib.  1085  Ib. 

is  7085  Ib.  net,  a  $6,50  per  100  Ib. 
Rule  XXXIII.  See  Pract.  Arith.  p.  110  Tare  &  Tret. 


3  Paid  for  repairs  on  Louse  in  Hanover-street, 
Rule  XII. 

19 


Bought  for  cash  1 20  gals,  rum  «$1 ,25  pr.  gal. 


Rule  VI. 


20. 


3  Sold  to  R.  Means,  150  c\vt.  sugar,  «§12,25 
Rule  I. 

24 


Received  of  Robert  Means,  his  note,  to  my 

order,  at  9  months,  with  interest,  in  full  for  150 
wt.  sugar          .          .  .... 

Rule  XLV. 


Sold  for  cash  3  hhds.H.  Lee's  tobacco,  \v'g.  as 
follows  ;  viz.  No.  13.      9212  Ib.  gross.  Tare  146  Ib. 

14.  8  3  27  138 

15.  10  1  13  148 


23  3  24  4U2  Ib. 

makes  2812  Ib.  net,  a  $6,90  per  100  Ib.      .     . 
Rule  XXXIII.     See  Pract.  Arith.  p.  110. 

27 


Paid    for    weighing    and    other  incidental 

charges  attending   the    delivery  of  Henry  Lee's 
tobacco  ...... 

Rule  XXXI I. 

30 


Paid  storage  of  H.  Lee's  tobacco.  15  hhds. 
Rule  XXXII. 

23* 


WASTE-BOOK. 


Boston,  March  30,  1817- 


J.  F. 


Furnished  H.  Lee  with  account  sales  of  his 

15  hhds.  tobacco,  amounting  to  §941,17,3 
My  commission  on  the  same  a  2£  per  cent.  25,88,2 
The  net  proceeds        ....         846,79, 

Rule  XXXIV.  See  Pract.  Arith.  p.  147. 

31 


Remitted  H.Lee,  by  mailjinbank  bills  ot'U.S 


Rule  XXXV 


April  4  • 


Bartered    with    R.  Means,    18   cwt. 

a  $12,50 

And  120  gallons  rum  a  gl,25 


suga 

225 
150 


,  For  20  casks  pot  ashes,  each  weighing 
2  2  qrs.  gross — tare  25  Ib.  pr.  cask 
is  45  2  4  Ib.  net>  a  $4,94,^ per  cwt.      $225 
500  yds.  tow  cloth,  a  ,25  125 

Rule  XXVI. 

6 


Rec'd  from  D.Jones,  pay't  of  his  note  $440 

Interest  for  30  days         .         .          .                2,05 
Rule  XVI.     N.  12.  


Paid  expenses,  this  quarter,  for  men's  wages 

and  other  incidental  charges 
Rule  XIII. 

10 


Chartered  the  Brig  Huntress,  Capt.  S.  Saw 

yer,  for  a  voyage  to  Bourdeaux,    and  laded   her 
with  the  following  goods  ;  viz. 
2200  bushels  corn,  boHof  C.  Lee,  a  $1  $2200 
2200  ditto  wheat,  bo'tof  C.  Lee,  a  $1,25  2750 


230  bags  coffee,  bought  of  E.  Nichols  & 
Son,  weighing  18400'  Ib.  a  ,25          . 
Cash  paid  for  dunnage,  &c.         .         . 
paid  shipping  charges         .         .         . 


4950 

4600 
175,20 
155 


Consigned  to  C.  Leroi,  Supercargo  for  sale  &  returns 
Rule  XXVIII. 


Made  Ensurance,  at  the  Union  Ensuratice 

Office,  Boston,  on  the  cargo  of  the  brig  Huntress 
from  Boston  to  Bourdeaux,  valued  $9880,20 
a  3f  per  cent,  premium         .         .         §370,50,7 
Policy          ...         75 

Rule  XXIII,     See  Pract.  Arith.  p.  148. 


$. 


C. 


872  67,1 
500 


350 


415 


120 


05 


25 


9880 


20 


371 


25,7 


WASTE-BOOK. 

Boston,  April  12,  1817. 


267 


J.  F. 

5 


Granted  to  C.  Lee  my  note,  dated  10th  inst.i 

at  60  days,  for  2200  bushels  corn  and  2200  do.  wheat!   4950 
Rule  XIX. 

15 


Bought   of  Richard    Lakeman    of    Ipswich, 

3400  quintals  of  merchantable  fish,  a  $3,50  $11900 
20  barrels  oil,  a  $10         .         .         .         .200 


For  which  I  paid  him  cash     .     .     .      $6050 

And  my  note,  at  60  days  for  the  rest      6050 

Rule"  IX.     Exp.  9.  

18 


12100 


Paid  Andrew  Newman,  in  full 
Rule  X. 
20 


Received  from  Joseph  Brigham,  cash  in  full 


for  5  hhds.  port  wine. 
Rule  XIV. 


24 


12100 
700 

275 


Paid  David  Whitman  in  full  for  1250  Ib.  tea' 


purchased  of  him  Feb.  18. 
Rule  X. 

26  - 


!   1562 


Paid  Winslow  Lamb  in  full 
Rule  X. 

28 


875 


Bought  of  Joseph  Turrel  for  cash  340  pairs 

men's  shoes,  a  ,90  per  pair         .          .          $306 
522  pairs  women's  coloured  ditto,  a  §1,20      626,40 
120  ditto  boots,  a  $3          .          .          .          360 
Rule  VI. 

May  4 


Received 

Rule  XVIII. 


of  William  Paterson's  bill 


Bo't  for  cash  8000  white  oak  staves  a  $35  pr.m. 


Rule  \ 


1292 


286 


280 


Shipped  on  board  the  General  Hamilton  for 

Oporto,  Capt.  A.  Delano,  and  consigned  to  F.  Al- 
vardo  &  Co.  for  sales  and  returns,  on  my  own  ac- 
count and  risk, 

3400  quintals  of  merchantable  fish  a  $3,50  §11900 
8000  white  oak  staves  a  $35          .           .           280 
Paid  shipping  charges         ....         11,50 
Rule  XXVIII.  


12191 


C 


50 


40 


62 


50 


268 


WASTE-BOOK. 


Boston,  May  15,  1817. 


S.  T. 

No. 

ion 

8.  T. 

No. 
Ia20 


Effected  Ensurance  at  the  Union  Ensurance 

Office,  Boston,  on  the  cargo  of  the  General  Ham- 
ilto'n,  from  Boston  to  Oporto  and  thence  to  Bos- 
ton, valued  $10000  a  5i  pr.  cent,  prera.  $525 

Policy      ....         ,75 

Rule  XXIII.  See  Pract.  Arith.  p.  148.  

, 18 — — 


Bought  for  cash  3  pipes  gin,  containing, 

No.  1.    134  gals.  7  out 

2.  129  8 

3.  133  5 


making  376  gals,  a  $1,55  pr.  gal. 
Rule  VI. 

20. 


396 


20 


Bought  of  R.  Means,  at  30  days,  20  casks  of 

pearl-ashes,  each  containing  2  1  26  Ib.  net,  mak- 
ing 49  2  16  Ib.  a  $6  per  cwt. 
Rule  VII. 

24 


Granted  to  R.  Means  my  note  dated  20th  inst. 

payable  in  30  days,  for  49  2  16  Ib.  pearl-ashes. 
Rule  XIX. 

31 


Shipped  on  hoard  the  Galen,  Capt.  S.  Turner 

for  London,  and  consigned  to  said  Capt.  for  sales 
and  returns,  the  following  goods  ;  viz. 

17  casks  of  Ashes,  pot,  marked  as  in  margin, 
w'g.  45  2  4  Ib.  net  a  $4,94  JL.  pr.  cwt.  $225 

20  do.  of  Ashes,  pearl,  marked  as  in  margin, 


weighing  49  2  16  Ib.  net,  a  $6  pr.  cwt.  297,85,7 
Paid  shipping  charges 
Rule  XXVII. 


15,25 


June  5 


Sold  for  cash  20  hbls.  oil,  a  $1 2,50  per  hi. 

'    Rule  II. 

10 


Received  from  Charles  Lee,  cash  in  full  . 
Rule  XIV. 


Paid  Charles  Lee  my  note,  dated  April  10th, 

at  60  days 

Rule  XVIII.     No.  15. 

18 


Sold  for  cash  2  punch,  rum,  a  S132  pr.  pun. 
Rule  II.  *  f     * 


o-j 


WASTE-BOOK. 


269 


Boston,  June  SO,  1817. 


G  Shipped  on  board  the  Mary-Ann,  Jas.  Sco 

Master, 


Bale 

.T.    V. 

Hhds. 
Ito20 

.T.  v.  I 


bound    to    Copenhagen — the    following 
goods  as  marked  in  the  margin  ;  viz. 

1  bale  broadcloth  containing   3000  yds.  bo 
of  Amasa  Goodhue  a  $3,50  per  yd.  $10500 
20  hhds.  tobacco  containing  240  cwt. 

bought  of  Thomas  Mackuy,  a  $5      1200 
Paid  shipping  charges  .  .  35 

Which  goods  are  consigned  to  Jacob  Vantorff,  mer 
chant  at  Copenhagen,  for  the  joint  concern  o: 
Samuel  Dean  and  eelf,  each  half, 

Rulr  XLII. 

2! 


Received  from  S.  Dean  his  half  of  the  value 

of  Voyage  in  Co.  to  Copenhagen 
Rule  XXXIX.      N.  38. 

DO  


7 


Sold  for  cash  3266  Ib.  coffee*  a  ,23  per  Ib. 
Rule  II. 

25 


7  Shipped  on  board  the  Pacific, Capt.L.  Davis 

for  New-Orleans, 

340  pairs  men's  shoes,  a  ,90         .         .         $306 
522  ditto  women's  coloured  ditto,  a  $1,20     626,40 
120  ditto  boots,  a  $3         .         .         .  360 

paid  shipping  charges,         .         .         .  10,2C 


jOrs-ic.-r.ed  to  Kinsman  Turrel,   merchant  there,  for 
ej-le  and  returns  on  my  own  account  and  risk,  vritb 
;     orders  to  invert  the  net  proceeds  in  produce, 
lilulc  XXVII. 

! 30 


7  Sold  .Tames  Wilson  1  puncheon  rum 
Rule  I. 

July  1 


Paid  house  expenses,  and  other  charges  thi 

quarter. 
Rule  XIII. 


Received  from  S.  Tyler  in  part  on  his  bond 


Rule  XVII. 


u  of  R.  Means,  balance  in  barter 

XIV. 


7  Paid  Richard  Lakeman  my  bill,  a  90  days 
Rule  XVIII.     N.  15. 


11735 

11?35 

5867 
914 


50 


48 


130260 

132 

119 

495 

25 

6050 


270 


WASTE-BOOK. 

Boston,  July  10,  1817- 


J.  F. 


Paid  Robert  Means  my  bill,  a  30  days    .  . 


Rule  XVIII.     N.  15. 


12 


Paid  Thos.  Mackay  in  full  for  tobacco  .    . 


Rule  X. 


15 


Bought   of  Rufus  Perkins  2500  Ib.   coftee 
a  22  cts.  .... 

Rule  VII. 


20 


7jPaid  Araasa  Goodhue  in  full  for  broadcloth 
Rule  X. 

: 25 


7. Sold  for  cash,  G75  Ib.  hyson  tea,  a  £1,50 
Rule  II. 


7  Sold  for  cash,  500  yds.  low  elotb,  «  25  cts. 
Rule  II. 

| 30 


Rec'd  Interest  on  W.Paterson's  bill,  41  days 
Rule  XV. 

August  1 


8  Granted  Rufus  Perkins  my  note,  a  30  days 
Rule  XIX. 


Paid  E.  Nichols  &  Son  cash  in  full  for  18400 
i      Ib.  coffee          ...... 

Rule  X. 

15 


8  Henry  Lee  of  Norfolk,  Virginia,  has  drawn 

on  me  in  favor  of  Charles  Lee,  for  $120  at  10  days 
after  sight,  which  draft  I  have  this  day  accepted 
Rule  XXXVI. 

18 


8  Sold  my  house  in  Hanover-street,  for  cash 

Rule  H.     N.  2. 

19  . 


8  Sold  for  cash  my  household  furniture  .  .  . 

j     Rule  II.     N.  2. 

20 


8  Remitted  Henry  Lee,  the  balance  of  his  act. 
Rule  XXXV.    ' 

! 25 


8 .Paid  my  acceptance  of  H.  Lee's  draft  in  fa- 
vor of  C.  Lee.          ..... 

Rule  XVIII.     Note  15 


I- 

297 


1200 

550 

10500 

1012 

125 

1 

550 

4600 

120 
3000 
2300 

226 


C. 

85,7 


50 


96 


79,1 


10] 


WASTE-BOOK. 


271 


Boston,  August  %8,  1817. 


J.  F. 

8 

8 
8 
8 

.8 
8 

8 

8 
9 

9 

Kiugman  Tnrrel,  writes  me  of  the  safe  ar- 
rival  at  New-Orleans,   of  the  Pacific,    with    my' 
goods  ;    the    net  proceeds  of  which  amounted  to 
§1405,  CO  —  that    he    had    invested    the    same    in! 
cotton,  which   he  had  shipped  by   return  of  the' 
Pacific,  on  my  account  and  risk,  9  bales  weighing 
6390  Jb.  a  ,<±2  per  Ib  
Rule  XXIX. 

°1                                                                        T 

$.     . 

1405 
1410 
550 

C. 
CO 

30 
50 
05 

75 

44 
80 

Sold  for  cash  120  barrels  flour,  a  $11,75  .  . 
Rule  11. 

ScYlf       1               i  '            ,       .  - 

Paid  Rufus  Perkins  my  bill,  a  30  days  .  .  . 

Rule  XVIII.     y.  15. 
cl 

The  Pacific,  Lemuel  Davis,  has  arrived  from 

New-Orleans,   and  brought   me  m  return  the  net! 
proceeds   of  my   goods,   remitted   by   K.   Turrel, 
merchant  there,  9  "boles  cotton,  weighing  G390  lb.; 
a  ,22  pr.  lb  1405 
Rule  XXX. 
\                                        ,.,.' 

Paid  for  freight  and  other  charges  for  my 

goods  in  the  Pacific  from  >.                     .         .                  134 
Rule  XXIV. 
12———.                                   ' 

Sold  for  cash  on  the  wharf  at  auction  my  9 

bales  of  cotton,  •                                                r  ^b. 
Rule  II.  &  XXIX.     IS.  27. 

1885 

833 
14 

Ii7 
876 

Sold  W.  Lamb  575  i 

for  which  I  received 
the  rest  at  60  days 
Rule  !!!.                                                                  
qn 

Received  from  Samuel  Tyler  SI  4  on  his  bond. 
Rule  XVII. 
Ocl   1 

Paid  for  men's   wages  aii'l  other  incidental 
expenses  this  quarter. 
Rule  XIII. 

r 

Sold  A.  Newman  3  pipes  g:a,  376  gallons, 

a  $1,80,  at  90  days. 
Rale  I. 

272 


WASTE-BOOK. 


Boston,  October  9,  1817. 


J-  F-l  $• 

9|Bonght  of  James  Wilson  for  account  of  Vender 

Effingin,  Amsterdam,  at  30  days, 
w      I          10  hhds.  tobacco,  weighing  as  follows  ;  viz. 
rvJ  No.  1.    1340  Ib.  eross— tare  84 Ib. 

2.  1574  .  .  .  .  90 
Shipped  on  board  3.  1394  ....  89 
the  Mary-Ann,  4.  1504  ....  96 
Capt.  Hoffman,  5.  1479  ....  88 
for  said  Effingin1  s  6.  1584  ....  87 
account  and  risk.  7.  1498  ....  90 

8.  1640     ....     100 

9.  1549       ....     99 
10.    1584     ....       98 


15146  Ib. 
921 


921  Ib. 


142251b.net  a$4pr.!001b.$569 

|  Shipping  charges         .....         21,10 

Commission  a  5£  per  cent.         .         .         .          28,45 

Rule  XXXVII.  

10 


9  j  Granted  to  James  Wilson  my  note,  dated 

inst.  at  30  days,  for  10  hhds.   tobacco,  bought  o 
him  for  account  of  Vender  Effingin,  for 
[Rule  XIX. 

15 


9|Received  advice  from  Francisco  Alvardo  and 

Co.  of  the  safe  arrival  of  the  General  Hamilton,  al 
Oporto,  that  they  had  received  my  goods,  and  had 
sold  the  same  for  cash,  amounting,  after  deducting 
freight,  duties,  &c.  to  14637,800  reas— Exchange 
a  §1,25  per  milrea ;  that  they  had  ship'd  by  the  re 
turn  of  the  General  Hamilton  for  Boston,the  net  pro- 
ceeds in  port  wine,  viz.  18297^  gals.  a800  reas  pr  gal. 


Rule  XXIX. 


See  Pract.  Arith.  p. 
20 


Exchange. 


9|Received  from  S.  Tyler,  S350  OQ 
Rule  XVII. 

05 


61 


569 


9  Sold  for  cash  400  yds.  linen,  a  ,95  per  yd. 
Rule  II. 

30 


9|S'd  J.Wilson  750  yds.  b'dcloth  a  §4,25 

for  which  I  received" my  note  pay'ble  to  him  $569 
Cash  for  the  rest,         ....         2618,50 
I  Rule  IV.  


8297 


380 


3187 


WASTE-BOOK. 


373 


Boston,  November  1,  1817. 


10 


10 


10 


10 


10 


The  Galen,  Capt.  Turner,  is  arrived  from 

London,  and  brings  me  in  return  for  my  goods,  " 
Pianos  Fortes,  valued  a  £l81,12,2f  Ster.     .     , 
Rule  XXIX.  N.  26.  See  Tract.  Arith.  p.  160. 
5 


Entered   at   the  Custom  House 

Pianos,  and  paid  duties,  freight,  &c. 
Rule  XXIV. 


my 


Fortes 


6 


Received  advice  from  Jacob  Vantortf,  of  Co- 
penhagen, that  he  had  received  by  the  Mary-Ann, 
Capt.  Scot,  the  goods  consigned  to  him  for  the 
joint  concern  of  Samuel  Dean  and  self,  amounting 
to  14786  rix  dollars  and  50  skillings,  Exchange 
100  cts.  per  rix  dollar.  .... 

Rule  XLI1I.     See  Pract.  Arith.  p.  171. 


Received  intelligence  from  Charles  Leroi, 

Supercargo  of  the  brig  Huntress,  who  advises  his 
safe  arrival  at  Bourdeaux,  that  lie  had  sold  the 
cargo,  amounting  to  74101  livres  10  sols,  Exchange 
20  cents  per  livre  ;  that  he  had  shipped  by  return 
of  the  Huntress  the  net  proceeds  in  brandy  ;  viz. 
11856-6_  gals,  a  6  liv.  5  sols  per  gal. 
Rule  XXIX.  See  Pract.  Arith.  p.  167. 

12 


The  brig  Huntress,  Capt.  S.  Sawyer,  is  ar- 
rived from  Bourdeaux,  and  brought  the  net  pro- 
ceeds of  my  adventure,  viz.  11856^  ga]s.  brandy, 
a  6  liv.  5  sols  per  gal.  .... 

Rule  XXX. 


17 


Entered,  at  the  Custoni-House,my  goodsfrom 

Bourdeaux,  and  paid  duties,  freight,  &c.      .     . 
Rule  XXIV. 

18 


807 


115 


16 


50 


14820 


14020 


784 


The  General  Hamilton,  Capt.  Delano,  is  ar- 
rived from  Oporto,  and  brought  returns  of  my  goods, 
viz.  18l297i  callous  port  wine,  a  800  reas  per  gal.  (18297 

Rule  XXX. 

19 


5aid  at  the  Custom-Hoese,  duties  and  other 

charges  for  the  General  Hamilton  from  Oporto 
Rule  XXIV. 

20 


deceived  from  Samuel   Tyler  g870  on  his 


bond. 
Rule  XVII. 


1010 


870 


48 


30 


40 


WASTE-BOOK, 


[13 


Boston,  November  Z5,  181?. 


J.  F. 

10 


10 

10 
10 

10 

10 

10 
10 

11 

ii 

11 


S'd.  for  cash  on  the  wharf  my  18297£  gallons 
port  wine,  a  $1 ,76  per  gal.  being  the  net  proceeds 
of  my  adventure  to  Oporto  by  the  General  Ham- 
ilton. ....  .  . 

Rule  XXIX.     N.  27. 


Received  of  Jones  &  Pennman  for  freight  oi 

the  ship  Massachusetts.          .... 
Rule  XXII. 


28 


Received  from  Winsiow  Lamb  in  full 
Rule  XIV. 


Paid  reimbursements  on  the  Massachusetts 
to  Europe  .  .  .... 

Rule  XII. 

30 ; 


Bought  of  11.  Means,  for  account  of  D.  Whit- 
man and  self  in  Co.  each  half,  340  cwt.  pot  ashes, 
a  $6  per  c\vt.  on  demand,  myself  having  the  dis- 
posal of  the  same. 

Rule  XXXIX. 

—  December  1 


Paid  R.  Means  in  full  for  our  340  cut.   pol 

ashes,  in  Co.  with  D.  Whitman  and  self.     .     . 
Rule  X. 

2 


Sold  for  cash  our  340  cut.  pot  ashes,  in  Co. 

with  D.  Wrhitman  and  self,  a  $6,75  per  cwt.  .  . 
Rule  XL. 


Received  from  D.  Whitman  his  half  share  ol 

ashes  bought  of  11.  Means. 
Rule  XXXIX.     N.  33. 

3 


Paid  charges  on  ashes  in  Co. 
Rule  XXXIX.     N.  36. 

4 


Adjusted  accounts  with  David  Whitman  in 

Co.  and  paid  him  in  part  of  net  proceeds  on  ashes 
in  Co.         .  .          .... 

Rule  XXXIX.     N.  40. 

5 


Adjusted  accounts  with  S.  Dean,  of  voyage 

in  Co.  to  Copenhagen,   and  paid  him  in  part  ol 
net  proceeds.          ...... 

Rule  XXXI X.     N.  40. 


32203 


14] 


WASTE-BOOK. 

'Boston 9  December  6,  1817. 


275 


J.    F. 
11 


11 


Received  from  Vender  Effingin  his  remit- 
tance, per  bill  on  R.  Perkins,  Boston,  for  amount 
of  goods  shipped  by  his  order,  on  board  the  Mary- 
Ann,  Capt.  Hoffman,  amounting  to  1855  gilders 
13  stivers,  Exchange  40  cents  per  gilder. 

Rule  XXXI.     bee  Pract.  Arith.  p.  166. 

8 


Received  from    Kiifus  Perkins,  payment  of 

Vender  Effingin's  bill.          .... 
Rule  XXXI.     X.  29. 

9 


Sold  for  cash  10  lihds.  port  wine,  a  851,50 
Rule  II. 
12 


Sold  for  cash  3266  !b.  coffee  a  ,20  per  Ib. 
Rule  I. 


Received  from  James  Wilson   in  full  for  1 

puncheon  of  rum         ..... 
Rule  XIV. 

14 


Andrew  Newman  is  become  a  bankrupt,  and 

owes  me         ...  .  g>G76,80 

He  has  compounded  with  his  creditors, 

a  ,38  on  a  dollar,  which  I  have  received 

in  full  of  his  debt.         .          .          .          257,18,4 


Balance  allowed  him 
Rule  XXI.     See  Pract.  Arith,  p.  127. 
15 


419,61,6 


Sold  at  auction  my  brandy  by  brig  Huntress 

from  BourcU  aux— Amount  of  saJLs         $'2C676 
From  which  deduct  commission  14  )  n 
United  States  duty         .       -       |  \  2  Per  ct"  53° 


Received  in  ciish         .  .  $13070,24 

(  James  Henderson's  note. 
Bills  ^  at  90  days,  endorsed  by 

receivable  j  William  Ponsby  $6535,12 

(  T.  Henshaw's  note,  at  90 
days,  endorsed  by  Tho.  Benson     .     6535,12 


Rule  XXXIX.     N.  27. 


16 


$26140,48 


11 


Sold  for  cash  3  Pianos  Fortes  a  $115  .  .  . 
Rule  II. 


$• 

742 

742 

515 

947 


14 


676 


26140 


48 


525 


WASTE-BOOK. 

Boston,  December  17,  1817. 


[15 


J.   F. 
11 


11 


Taken  for  the  use  of  my  family  1  Piano  Forte 

Rule  VI.     N.  4. 


12 

12 

12 
12 

12 
12 

12 
12 


&l  the  request  of  Robert  Means,  I  have  ac- 
commodated him  by  a  renewal  of  his  note,  due 

:his  day,  for  4  months  longer,  .  .  J§1837,50 
His  bill  renewed  for  the  same. 

Rule  XVIII.  obs. 


Received  from   Samuel  Tyler,  the  balance 
due  on  his  bond.         .         .          .  g271 

Amount  of  Interest  by  partial  payments    86,34,4 

Rule  XVI.  See  Pract.  Arith.  p.  144.  

25 


Received  from  Jacob  Vantorff,  merchant,  at 

Copenhagen,  the  net  proceeds  of  goods  consigned 
to  him  for  the  joint  concern  of  Samuel  Dean  and 
self,  each  half,  by  the  Mary-Ann,  Capt.  Scot, 
amounting  to  14786  rix  dollars  and  50  skillings, 
Exchange  100  cents  per  rix  dollar. 
Rule  XLIV.  See  Pract.  Arith.  p.  171. 

20 


Sold  Vancouver  &  Sons  the  ship  Massachu- 
setts, at  4  months        ..... 
Rule  I. 


Received  from  Vancouver  &  Sons  (heir  bill 

payable  in  4  months,  for  the  ship  Massachusetts 
Rule  XLV. 

27 


Sold  fnr  cash,  2  Piano  Fortes,  a  $210 
Rule  II. 


Rec'd.  payment  of  A.Eastman's  bill  $475 

Interest  on  the  same  for  11  months      .      26,12,5 
Rule  XVI.     N.  12. 

30 


Paid  for  men's  wages,  and  other  expenses 
this  quarter.         ...... 

Rule  XIII. 


S'd.  for  cash,  household  furniture,  1  P.  Forte 
Rule  II. 


Received  from  Robert  Means,  Interest  on  his 

note,  for  9  months  and  0  days         .         ,         , 
Rule  XV. 


14786 


WASTE-BOOK. 


S77 


Boston,  December  31,  1817- 


13 


Profit  &  Loss  to  be  debited  for  sundries, 
Expense  account  since  Jan.  1,  $499,33 

For  men's  wages  and  other  charges     .     .  .    120,25 

ditto 119,24 

ditto 127,44 

ditto 132,40 


Profit  &  Loss  to  be  credited 

articles  of  gain,  since  Jan.  1, 
For  House,  in  Hanover-street 

Land,  in  Washington  Comity 

Ship  Massachusetts 

Household  Furniture 

Broadcloth 

Linen         .... 

Port  wine 

Sugar         .... 

Ruin         .... 

Gin 

Coffee         .... 
Flour  .... 

Tea         .... 

Oil 

Piano  Fortes 
Commission 
Voyage  to  Bourdeaux 

London         .         . 

New-Orleans 

from  New-Orleans 

Vender  Effingin,  Amsterdam 
Voyage  from  Bourdeaux     .     . 
Oporto 


for  sundries, 

$42916,15,8 
.      $455,63 
.     .      262,50 
3557,24 
,      .       810 

562,50 
520 
139 
549,50 
111 
94 

303,62 
510 
283,75 

50 
347^84 

54,33,2 
4568,84,3 
.   5580 
.   153,55,3 
103,20 
344,75 
.   123,71 
.   10535,68 
12895,51 


Profit  &  Loss  to  be  finally  debited  per  Stock, 

For  net  gain  since  January  1, 


Balance  account  to  be  debited  for  Stock, 

For  net  Stock          ..... 

END  OF  THE  WASTE-BOOK. 


24* 


42916  15,8 

43796 1 92,1 


61834 


278 


JOURNAL. 


Boston,  January  1,  18  iy. 


Dr. 
L.  F. 

1 

3 

3 

3 
3 

2 

4 
4 
4 
4 
4 
4 
5 

Cr. 

L.  F. 

1 

Sundries  Dr.  to  Stock  $22527,50 
Cash  deposited  in  the  Union  Bank  .  $4000 
House  in  Hanover-street         .       .         2500 
Lands  for  750  acres  in  County  of  Wash- 
ington, P.  of  Maine,  a  ,75  per  acre     562,50 
Ship  Massachusetts      .         .         .         7000 
Household  furniture      .         .         .        1500 
Xotes  receivable, 
J.  Thomsons  note,  dated  Nov.  10  last, 
payable  to  ray  order,  at  6  months  $350 
D.Jones'  note,  dated  Dec.  3d  last, 
payable  to  my  order  tit  3  months,  410 
760 
Broadcloth  250  yds.  a  $3,50  per  yd.       875 
Linen,  400  yards,  a  ,80         .         .          320 
Port  wine,  7  hhds.  a  g45  per  hhd.         315 
Sugar,  20  hhds.  w'g.  240  cwt.  a  $10,50  2520 
Rum,  12  puncheons,  a  $125  per  pun.  1500 
T.  Lamson,  mer.  Boston,  owes  me         400 
A.  Locke,  carpenter,  Salem,  owes  me  275  — 

$. 
22527 

C. 

50 

1 

5 
5 
5 
5 

Stock  Dr.  to  Sundries  g4490 
To  J.  Lewis,  mer.  Boston,  due  to  him  jg!40 
Lemuel  Samson,  mer.  Boston,  ditto  800 
James  Munson,  mer.  Boston,  ditto  2050 
Jos.  Franklin,  mer.  Boston,  ditto      1500  — 

4490 

7 

4 

Charles  Lee  Dr.  to  sugar, 

For  72  cwt.  a  g!2,50  per  cwt. 

900 

I 

4 

Cash  Dr.  to  rum, 

For  9  puncheons,  a  gl35  per  pun. 

1215 

b 

1 

James  Lewis  Dr.  to  cash, 

140 

1C 

4 

1 

Port  wine  Dr.  to  cash, 

For  8  hhds.  a  $42  per  hhd. 
18 

336 

4 

7 

Linen  Dr.  to  Andrew  Newman, 

For  1000  yards,  a  ,70  per  yd.         .      .      . 

700 

4 

1 

Sugar  Dr.  to  cash, 

For  84  cwt.  a  glO,72,6-JL  per  cwt.      . 

901 

5 

4 

Coffee  Dr.  to  sugar, 
Received  4032  Ib.  a  ,25  per  Ib.  in  barter  for  84 
cwt  sugar,  a  $12  per  cwt  

1008 

2] 


JOURNAL. 

Boston,  January  24,  1817. 


379 


Dr. 
L.  F. 
5 

Or. 
L.  F. 

1 

Joseph  Franklin  Dr.  to  cash, 
Paid  him  in  full         ..... 

S- 

1500 

Co 

5 

1 

n     " 

James  Mnnson  Dr.  ta  cash, 

2050 

1 
* 

3 

Smuiiies  Dr.  to  land  g825 

Cash  in  part  for  750  acres  land             jg350 
Biih  receivable,  bill  on  A.  Eastman,  at 
11  months,  with  interest,  the  rest       475 

00 

825 

5 

1 

Lemuel  Samsaii  Dr.  to  cash, 
Paid  him  in  full         ..... 
on 

800 

1 

4 

Cash  Dr.  to  Thomas  Lamson, 

Received  from  him  in  full         .      :  "V^^^H 
31 

400 

1 

5 

Cash  Dr.  to  Amos  Locke, 

Received  from  him  in  full 

275 

7 

1 

Samnol  Tyler  Dr.  to  cash, 

Lent  him  on  bond,  at  6  per  cent,  per  an. 

c 

2000 

1 

2 

Cash  Dr.  to  bills  receivable, 

Received  from  J.  Thomson  payment  of  his  note 

350 

1 

4 

Cash  Dr.  to  linen, 

For  400  yards  a  §1,10  per  yd. 
l« 

440 

7 

4 

Joseph  Brigham  Dr.  to  port  wine, 

For  5  hhds.  a  g55  per  hhd. 

275 

5 

1 

Flour  Dr.  to  cash, 

For  220  barrels,  a  $8,75  perbbl. 
18 

1925 

6 

8 

Tea  Dr.  to  David  Whitman, 

For  1250  Ib.  a  gl.25  per  Ib. 

Of) 

15621 

50 

3 

1 

Ship  Massachusetts  Dr.  to  cash, 

For  repairs,  paid  to  William  Hart 

00 

53 

20 

4 

1 

8 

Broadcloth  Dr.  to  sundries  g!750 
For  500  yds.  a  g>3,50  per  yd. 
To  cash,  in  part         .         .         g875 
Winslow  Lamb  for  rest         .        875 

1750 

380 


JOURNAL. 


Boston,  February  %5f  1817. 


Cr. 
L.  F. 

4 

2 
1 

1 
8 
6 

1 
8 
1 
1 
4 
8 
8 

Bills  receivable  Dr.  to  linen, 

For  600  yds.  a  gl,20  sold  to  Nye  Freeman,  for 
which  I  have  received  a  bill  on  A.  Young,  due 
at  90  days         ..... 

°6 

Sundries  Dr.  to  bills  receivable,  $720 
Cash,  recM.  for  A.  Young's  note,  disc'd.  §708,84 
Profit  and  Loss,  discounted  3  mo.  Inter.     11,16 

00 

Ship  Massachusetts  Dr.  to  cash, 

For  Ensurance  from  Boston  to  London  on  §6000 
at  3%  per  cent,  premium,     .     .     .      §210 
Policy,         .         .       .        ,75 

i\Iarch  1 

B.  Lee's  account  of  tobacco  Dr.  to  cash. 

Paid  freight  of  15  hhds.  from  Norfolk      . 

Bills  receivableDr.toH.Lee'sac't  tobacco 

Received  William  Paterson's  bill  a  3  months, 

Cash  Dr.  to  flour, 

For  100  barrels  a  $10,25 
10 

Henry  Lee's  ac't.  tobacco  Dr.  to  cash, 

Paid  truckage  15  hhds.  a  ,75  per  hhd. 
11 

Cash  Dr.  to  Henry  Lee's  ac't.  tobacco, 

For  8  hhds.  as  per  Waste,  wt.  7085  Ib.  net.    . 
1° 

House  in  Hanover-street,  Dr.  to  cash, 

10 

Rum  Dr.  to  cash, 

For  120  gallons,  a  $1,25 
20 

Robert  Means  Dr.  to  sugar, 

150  cwt.  a  $12,25  per  cwt. 
04 

Bills  receivable  Dr.  to  Robert  Means, 

Received  his  note,  a  9  months,  with  interest, 

Cash  Dr.  to  Henry  Lee's  tobacco, 
For  3  hbds.  wt.  2812  lb.net,  a  $6,90  per  100  Ib. 

JOURNAL. 


281 


Boston,  March  2?,  1817. 


Dr.    |   Cr. 
L.  F.'L.F. 


Henry  Lee's  ac't.  tobacco  Dr.  to  cash, 

'aid  for  weighing  and  other  charges, 

30 


flenry  Lee's  ac't.  tobacco  Dr.  to  cash, 

Paid  storage,          ..... 


H.L's  ac't.  (obae.  Dr.  to  simd's.  $872,67,3 

8  To  his  accH.  current  for  net  proceeds,  $846,79,1 

9  Commission  acH.  for  ;ny  commission,     25,88,2 


HL  Lee  his  aecount  current  Dr.  to  cash, 

Remitted  him  by  mail  in  bank  bills, 
April  4 


rl.  Means  Dr.  to  sundries.  §375 

Sugar,  1G  cwt.  a  $12,50 
Rum,  120  gallons,  a  $1,25 
Delivered  in  barter. 


150 


g  Sundries  Dr.  to  Robert  Means,  g>350 
Ashes,pot,  45  2  4  Ib.  a  $4,94  J»T     .    .  §225 
Tow  cloth,  500  yds.  a  ,25         .         ,         125 
Received  in  barter. 
6 


Cash  Dr.  to  sundries,  §412,05 

2  To  bills  receivable,  on  D.  Jones      .       §410 
Profit  and  Loss,  for  interest  30  days,        2,05 


17 

Expense  account  Dr.  to  cash, 

Paid  men's  wages,  &c.  this  quarter, 
10 


Voyage  to  Bnur'x.  Dr.  to  sund's.  $9380,2( 
7  To  C.  Lee,  for  2200  bush,  corn  a  §1        2200 
ditto,  2200  do.  wheat  a  $  1 ,25  2750 


To  E.  Nichols  &  Son,  for  230  bags  coffee 

wt.  18400  Ib.  a  ,25  per  Ib. 
Cash,  for  shipping  charges, 


4950 

4600 
330,2< 

By  brig  Huntress,  consigned  to  C.  Leroi,  fo 
sale  and  returns. 


Voyage  to  Bourdeaux  Dr.  to  cash, 

Premium  on  the  Huntress1  cargo  $9880,20 
a  3£  per  cent.        .        .        .         $370,50. 
Policy,  ,75 


JOURNAL. 

Boston,  April  1%,  1817. 


F. 

2 
8 

1 
g 

1 

7 
1 
1 
1 

2 
1 

6 

Charles  Lee  Dr.  to  bills  payable, 

Granted  him  my  note  10  inst.  a  60  days,      . 

$• 

4950 

2100 

2100 
700 
275 
1562 
875 

1292 
286 
280 

12191 

C. 

50 

40 

62 

50 

Sundries  Dr.  to  R.  Lakeman,  $12100 
Fish  merch'ta.  a  g3,50  per  quin.  3400  $1  1900 
Oil,  a  $10  per  bbl.  20  barrels,          .          200 

Richard  Lakeman  Dr.  to  sundries,  12100 
To  cash,         .         .         .         .         .         6050 

Bills  payable,  my  note  a  90  days,      .      6050 

JO 

Andrew  Newman  Dr.  to  cash, 

"0 

Dash  Dr.  to  Joseph  Brighara, 

leceived  from  him  in  full. 

David  Whitman  Dr.  to  cash, 

Paid  him  in  full  for  1250  Ib.  tea,  a  $1,25 
$6 

Winslow  Lamb  Dr.  to  cash, 

Paid  him,  balance.          .... 

00 

Sundries  Dr.  to  cash,  g!292,40 
<  Shoes,  a       ,90     340  pairs,         .         $306 
<  ditto,    a   $1,20     522  ditto,           .         626,40 
Boots,  a   $3          120  ditto,         .           260 

Cash  Dr.  to  bills  receivable, 

Received  payment  of  William  Paterson's  bill, 

Staves  Dr.  to  cash, 

For  8000  white  oak,  a  §35  per  M. 

Voyage  to  Oporto  Dr..to  sund's.  §1  219  1  ,50 

To  fish,  3400  quintals,  a  £3,50       .     §11900 
Staves,  8000  a  $35  per  M.           .         280 
Cash  paid  shipping  charges,           .         11,50 

Shipped  the  above  goods  on  board  the  Genera 
Hamilton,    Capt.    Amasa  Delano,    and  con 
signed  to   Francisco  Alvardo  &  Sons,  mer 
chants  at  Oporto,  for  sale  and  returns. 

•A 

JOURNAL. 


S83 


Boston,  May  15,  18J7- 


Dr. 

L,.     F. 

10 
5 
6 
8 
10 

2 
10 

'r. 
.F. 

1 
1 

8 
2 

6 

1 

6 

r 

royage  to  Oporto  Dr.  to  cash, 

ror  premium  on  the  General  Hamilton's  cargo, 
13 

$• 

525 

582 
297 
297 

533 

250 
900 

4950 
26 

1173 

536 
586 

5 

0 

5,: 
s," 

10,' 

50 

50 

xin  Dr.  to  easli, 
por  376  gals,  a  $1,55  per  gal. 
°O 

Ashes,  pearl,  Dr.  to  Robert  Means, 

For  20  casks,  wt.  49  2  16  lb.  a  $6  per  cwt. 

n,                                                                        °1 

iobert  Means  Dr.  to  bills  payable, 

ror  my  note  granted  him  for  30  days, 
31 

Voyage  toLondonDr.to  sund's.  $538,10,7 
(To  Ashes  pot,  45  2  4  lb.  «  $4,94-0- 
S  per  cwt.               .               .                   $225 
f      Ashes  pearl,  49  1  16  lb.  a  $6         297,85,7 
Cash  paid  shipping  charges,        .       15,25 

Shipped  on  board  the  Galen,  S.  Turner  master, 
for  London,  and  to  him  consigned,  for   sale 
and  returns,  for  iny  account  and  risk. 

Cash  Dr.  to  oil, 

For  20  barrels  a  $12,50  per  bar. 

3ash  Dr.  to  Charles  Lee, 

deceived  from  him  in  full, 

•n 

Bills  payable,  Dr.  to  cash, 

?  *d  rny  note  to  C.  Lee,  dated  April  10,  at  60  day 
-to 

Dash  Dr.  to  rum, 

For  2  puncheons  a  R132  per  puncheon,     .     . 

°o 

Voyage  to  Copenhagen  in  Co.  with  8.  Dean 
and  self,  each  half,  Dr.  to  sund's.  $11735 
To  Amasa  Goodhue,  for  3000  yds.  broadcloth 
a  $3,50  per  yd.      .         .         .         $10500 
To  Thomas  Mackay,  for  240  cwt.  to- 
bacco, a  $5  per  cwt.         .         .           1200 
Cash  paid  shipping  charges,       .         .         35 

Consigned  to  Jacob  Vantorff,  merchant  there. 

Samuel  Dean's  account  current  Dr.  to  his  ac 
count  in  Co.  for  half  the  above  goods.     .     . 

Cash  Dr.  to  S.  Dean  his  ac't,  current, 
For  his  half  of  voyage  in  Co.  to  Copenhagen,  . 

JOURNAL. 


Boston,  June  23,  1817- 


Dr. 
L.  F» 

1 

11 

9 

10 
i 
i 

2 
2 
9 
5 

9 
1 

1 
1 

Cr. 
L.  F. 
A 

6 

6 
1 

4 

1 
7 
8 
1 
1 
1 
9 
1 
6 
6 
3 

Cash  Dr.  to  coffee, 

For  3266  Ib.  a  ,28  per  Ib. 

°5 

$. 
914 

1302 

132 
119 
495 
25 
C050 
297 
1200 
550 
10500 
125 
1012 
1 

C. 

48 

60 

24 

85,7 

50 
96 

Voy.  to  N.Orleans  Dr.  to  sund's.  $1  302,60 
<  To  Shoes  men's,  340  pairs,  a  ,90        $30G 
{        do.  women's  522  pairs,  a  $1,20         626,40 
Boots,  120  pairs,  a  $350         .          360 
Cash,  paid  shipping  charges,       .       10,2C 

Consigned  to  Kingman  Turrel,  merchant  there. 
30 

James  Wilson  Dr.  to  rum, 
For  1  puncheon,  a  $132 

JUIV      1                                                          r- 

Expense  ae't.  Dr.  to  cash, 

Paid  this  quarter,  for  men's  wages,  &c.     .     . 

0 

Cash  Dr.  to  Samuel  Tyler, 

Received  from  him  in  part,  lent  on  bond, 
3 

Cash  Dr.  to  Robert  Means, 
Received  from  hmi,  balance  in  barter, 
6 

Bills  payable  Dr.  to  cash, 

Paid  to  Richard  Lakeman  my  bill, 
10 

Bills  payable  Dr.  to  cash, 

Paid  Robert  Means  my  bill  at  30  days, 

10 

Thomas  Mackay  Dr.  to  cash, 

Paid  him  in  full,         .                    .             , 
15 

Coffee  Dr,  to  Rufus  Perkins, 

For  2500  Ib.  a  ,22  per  Ib.         .     '     . 
20 

Amasa  Goodhue  Dr.  to  cash, 

°5 

dash  Dr.  fo  tow  cloth, 

For  500  yds.  a  ,25         ... 

Cash  Dr.  to  tea, 
For  675  Ib.  hyson,  a  gt,50 
30 

Cash  Dr.  to  Profit  and  Loss, 
"or  interest  on  W.  Patersou's  note,      ... 

8j 


JOURNAL. 


2S5 


Boston,  August  1,  1817. 


Cr. 
L.F. 
2 

2 

2 

3 
3 
2 

2 
11 

F) 
2 
12 

2 
11 
6 

7 

Rufus  Perkins  Dr.  to  bills  payable, 

Paid  my  note  a  30  days, 

8- 

550 

4600 

120 
3000 
2300 

226 
120 

1405 
1410 
550 

1405 
134 
1885 

833 

14 

£.  Nichols  &  Son  Dr.  to  cash. 
For  18400  Ib.  coffee, 

H.  Lee's  ae'f.  cur't.  Dr.  to  bills  payable, 

Accepted  his  draft  on  me,  at  10  days  after  sight, 
1° 

Cash  Dr.  to  house  in  Hanover-street, 

Cash  Dr.  to  household  furniture,     .     . 

Of) 

Henry  Lee's  ae't.  current  Dr.  to  cash, 

Paid  him  balance  in  full  of  his  account,     .     . 
05 

Bills  payable  Dr.  to  cash, 

Paid  my  acceptance  to  H.  Lee, 

K.  Torre!,  my  ac't.  cur't.  Dr.  to  voyage 

to  Xew-Orleans, 
For  net  proceeds  of  goods  consigned  to  him,    . 
31 

Cash  Dr.  to  flour, 
For  120  barrels,  a  $11,75 

Bills  payable  Dr.  to  cash, 

For  my  bill  to  R.  Perkin?,  a  30  days,      .     . 
3 

Voyage  from  New-Orleans   Dr.   to   K. 

TurrePs  account  current, 
For  9  bales  cotton,  wt.  6390  Ib.  a  ,22  per  Ib. 

Voyage  from  New-Orleans  Dr.  to  cash, 

Paid  freight  and  other  charges, 

Cash  Dr.  to  voyage  from  New-Orleans, 

For  6390  Ib.  cotton,  a  ,29$  per  Ib.         .     . 

CVJ 

Sundries  Dr.  to  tea,  g833,75, 
Cash  in  part,             .             .          .         §578,75 
Winslow  Lamb  rest  at  60  days^      .     .     255 

<>A 

.Cash  Dr.  to  S.Tyler,  in  part,  lent  on  bond, 

386  JOURNAL. 

Boston,  October  1,  1817. 


Dr. 
,.  F. 

10 

7 
11 

9 
11 

1 
1 

1 

2 

7 
10 
11 

11 

Cr. 
L.  F. 
2 

5 

9 
2 
9 

2 
10 

7 
4 
4 

10 

2 
10 

10 

Expense  account  Dr.  to  cash, 

Paid  men's  wages,  &c. 
5 

$. 
127 

676 

-618 

569 

18297 
350 
380 

3187 
807 
115 

14786 
14820! 

C. 

44 

80 
55 

25 

50 
16 
30 

48 
30 

Andrew  Newman  Dr.  to  gin, 

For  376  gals,  a  $1,80,  payable  in  90  days,     . 
9 

Vender  Effingin  his  account  current  Dr. 

to  sundries,  $618,55. 
To  J.  W.  14225  Ib.  tobac.  a$4  per  100  Ib.  $569 
Cash,  paid  for  shipping,        .      .       .      21,10 
Commission,  for  my  commission,    .    .    28,45 

Shipped  on  board  the  Mary-Ann,  Capt.  Hoffman, 
for  Amsterdam,  per  order,  and  for  account 
and  risk  of  said  Effingin. 
10 

James  Wilson  Dr.  to  bills  payable, 

For  my  note  dated  9  inst.  at  30  days, 

Francisco  Alvardo  &  Co.  his  ac't.  cur't. 

Dr.  to  voyage  to  Oporto, 
For  net  proceeds  of  goods  consigned,      .     . 

°o 

Cash  Dr.  to  Samuel  Tyler, 

Received  in  part,  on  bond, 
°5 

Cash  Dr.  to  linen, 

For  400  yds.  a  ,95 
30 

Sundries  Dr.  to  broadcloth,  $3  187,50 
Cash,  in  part,         .           .           .             $2618,50 
Bills  payable,  my  note  a  90  days,       .      569  — 

Piano  Forte  Dr.  to  voyage  to  London, 

For  6,  valued  at  £18J,12,2|  sterling,       .       . 
5 

Voyage  to  London  Dr.  to  cash, 

Paid  duties  at  the  custom  house  and  freight,    . 
a 

Jacob  Vantorff  our  ac't.  current  Dr.  to 

voyage  in  Co.  to  Copenhagen, 
For  net  proceeds,  as  per  account  of  sales,  amount- 
ing to  14786  rix  dols.  and  50  skillings, 
8 

Charles  Leroi  my  account  current  Dr.  to 

voyage  to  Bourdeaux, 
For  net  proceeds  per  brig  Huntress,  amounting  to 
11856JL  gals,  brandy,  a  6  liv.  5  sols,     .     . 

10] 


JOURNAL. 


887 


Boston,  November  12,  18i7- 


Dr. 
I..  F. 
11 

11 

12 

11 
1 
1 

1 
1 

Q 

L. 

12 
12 

8 
< 
< 

(Jr. 
L.  F. 
11 

2 
11 

2 
7 
11 

0 

8 
2 
8 

12 

2 
12 

12 

Voyage  from  Bourdeaux  Dr.  to  C.  Leroi 

my  account  current, 
^or  net  proceeds  of  voyage  to  Bourdeaux,     . 
-19 

8- 

4820 
784 

8297 
1010 
870 
32203 
5054 
255 
1208 
2040 

1020 
204C 

2295 
102C 

C. 

0 
0 

25 
40 

16 

39 

20 

Voyage  from  Bourdeaux  Dr.  to  cash, 

3M  duties  at  custom  house  and  freight  on  brandy, 
18 

Voyage  f.  Oporto  Dr.  to  F.  Alvardo  &  Co. 

For*  net   proceeds   by   the  General  Hamilton, 
18297^  gals,  port  wine,  a  800  reas  per  gal. 
19 

Voyage  from  Oporto  Dr.  to  cash, 

Paid  duties,  freight,  &c. 

°o 

Cash  Dr.  to  Samuel  Tyler, 

deceived  in  part  on  his  bond, 

Cash  Dr.  to  voyage  from  Oporto, 

For  182973-  gals,  port  wine,  a  $1,76     .      . 

0*7 

Cash  Dr.  to  ship  Massachusetts, 

For  freight  from  Europe,  &c. 
«3 

Cash  Dr.  to  Winslow  Lamb, 

Ship  Massachusetts  Dr.  to  cash, 

Paid  the  Capt.  for  reimbursements, 
-  30 

Ashes  in  Co.  with  D.  W.  Dr.  to  R.  Means 

For  340  cwt.  ashes,  pot,  a  $6,  on  demand,     . 

David  Whitman's  account  current  Dr. 

To  his  account  in  Cc.  for  his  half  of  the  above 
mentioned  pot  ashes,       

Dec    1 

Robert  Means  Dr.  to  cash, 

Paid  him  in  full  for  340  cwt.  p  ot  ashes,  bo1t  of  him 
in  Co.  with  D.  Whitman  and  self,  each  half, 

Cash  Dr.   to  ashes,  in  Co.  v/lth  David 

Whitman  and  self, 
For  340  cwt.  &  ^6,75  per  cwt.             ... 

Cash  Dr.  to  D.  Whitman,  his  ac't.  cur'( 

Received  hjs  half  share  of  our  340  cwt.  pot  ashes 

388 


JOURNAL. 


Boston,  December  3,  18 1 7. 


Cr. 
L.F. 

2 

2 
2 
11 
2 
4 
5 
9 
7 

11 
i 

r 
11 

Ashes  in  Co.  with  David  Whitman  and 

self,  each  half,  Dr.  to  cash, 
For  charges  on  the  same,        .... 

$. 

86 
1020 
6867 

742 
742 
515 
947 
132 

676 

26140 
525 
210 

14786 

C. 

70 

50 
26 
26 

14 

80 
48 

43 

David  Whitman's  ae't.  in  Co.  Dr.  to  cash. 

F'd  him  in  part  for  his  share  of  net  proc's  on  ashes, 
5 

Sam.  Dean's  account  in  Co.  Dr.  to  cash, 

Paid  him  in  part  for  his  share  of  net  proceed?, 

Sills  rec'able  Dr.  to  V.Effingin's  ae't.  cur. 
i^or  bill  remitted,  in  full  for  net  proceed?,  on  R.  P. 
£ 

Sash  Dr.  to  bills  receivable, 

To  Vender  Effingin's  bill  on  Rufus  Perkins,    . 

,,.„  _,.  „ 

Dash  Dr.  to  port  wine, 

For  10  hhds.  a  $51,50  per  hhd. 

in 

Cash  Dr.  to  coffee, 

For  3266  Ib  a  29  per  Ib        

13 

Cash  Dr.  to  James  Wilson, 

For  1  puncheon  rum, 
14 

Sundries  Dr.  to  A.  Newman,  $676,80, 
Cash,  received  in  composition,    .    .     $257,  18,^ 
Profit  and  Loss  —  for  balance,  loss,      .     419,61,6 

1C 

Sundries  Dr.  to  voyage  fr.  Bourdeaux,$26  140,48 

Cash,  in  part,  for  sales  of  brandy  at  auction,     .     D.  13070,  '24 
!  James  Henderson,  for  his  note  a  3  mo. 
endorsed  by  W.  Ponsby,         ,         .      6535,12 
Thomas  Henshaw's  note,  a  3  months, 
endorsed  by  Thos.  Benson,          .          6535,1- 

Cash  Dr.  to  Piano  Fortes, 

For  3  a  $175, 
'17 

Household  furniture  Dr.  to  Piano  Fortes 

For  1  taken  for  family  use, 
IS 

Cash  Dr.  to  J.  Vantorff  our  ae't.  current, 

For  net  proceeds   of  goods   consigned   for   the 
joint  concern  of  Samuel  Dean  and  self,     . 

JOURNAL. 


Boston,  December  20,  1817. 


Dr. 
L.  F 

8 


Cr. 
L.  F 


12 

2 
2 
2 

10 
2 
2 


12 


Robert  Means  Dr.  to  bills  receivable, 

For  his  bill  given  up  for  renewal  this  day,     . 

Bills  receivable  Dr.  to  Robert  Means, 
For  his  bill  renewed  for  4  months, 


Cash  Dr.  to  sundries,  $357,34,4 

To  Samuel  Tyler,   for  balance  principal  due  on 

his  bond,         .         .  .          $271 

Profit  and  Loss,  for  interest,         .      86,34, 


25 


Vancouver  &  Sons  Dr.  to  ship  Massa. 

For  said  ship,  a  4  months, 

26 , 


Bills  receivable  Dr.  to  Vancouver  &Sons 

For  ship  Massachusetts,  a  4  months, 

27 


Cash  Dr.  to  Piano  Fortes, 

For  2  a  $210, 

28  


Cash  Dr.  to  sundries,  §501,12,5 
Bills  receivable,  Abram  Eastman's, 
Profit  and  Loss,  for  iaterest  11  mo. 


$475 
26,12,5 


30 


2  Expense  account  Dr.  to  cash, 

For  men's  wages,  &c.  this  quarter, 


Cash  Dr.  to  household  furniture, 


for  1  Piano  Forte, 


ash  Dr.  to  Profit  and  Loss, 
For  interest  on  Robert  Means*  bill  for  9  month 

and  6  days, 

31  . 


Profit  and  Loss  Dr.  to  sundries,  $499,33 
To  expense  account  for  men's  wages,  &c. 

$120,25 

ditto, 119,24 

ditto, 127,44 

ditto, 132,40 


25* 


890 


JOURNAL. 


[13 


Boston,  December  31,  1817- 


Dr. 
JU.  F. 

Cr. 
L.F. 

$• 

C. 

3 

SundriesDr.to  Profit  &Loss,  $42916,15,8 

3 

To  House  in  Hanover-street,     .       g    455,63 

3 

Land  in  the  Coun.  of  Washing'n.       262,50 

3 

Ship  Massachusetts,           .                3557,24 

3 

Household  furniture,         .         .         810 

4 

Broadcloth,          .         .           .             562,50 

4 

Linen,         ....           520 

4 

Port  wine,     ....           139 

4 

Sugar,          ....           589,50 

- 

4 

Rum,          .         .          .           .             Ill 

5 

Gin,          94 

5 

Coflee,         ....            303,62 

5 

Flour,             .          .          .         .         510 

6 

Tea,         ....               283,75 

6 

Oil,         50 

7 

Piano  Fortes,         .         .         .            347,84 

9 

Commission  account,         .         .          54,33,2 

10 

Voyage  to  Bourdeaux,          .           4568,84,3 

10 

Oporto,         .          .          5580 

10 

London,         .         .           153,55,3 

11 

New-Orleans,         .           103,20 

11 

Voyage  from  New-Orleans,       .         344,75 

11 

Vender  Effingin,  of  Amsterdam,        123,7  1 

11 

Voyage  from  Bourdeaux,       .         10535,68 

12 

Oporto,                     12895,51 

42916 

15,8 

3 

1 

Profit  and  Loss  Dr.  to  stock, 

For  net  gain  sinee  January  1, 

43796 

92,1 

12 

Balance  ac't.  Dr.  to'sund's.  $63444,31  ,1 

2 

To  cash,         ....          $41561,57,1 

2 

Bills  receivable,         .                    21882,74 

63444 

31  1 

v*->*i*i*i 

JJ,4 

12 

Sundries  Dr.  to  balance  ac't.  §63444,31,1 

| 

Samuel  Dean's  ac't.  in  Co.  $1525.74 

12 

D.  Whitman's  ac't.  in  Co.        84,15 

1609,89 

1 

Stock,  net  of  my  estate,                     6  1  834,42,  1 

—      ,    .  

63444 

31,1 

1 

Stock  Dr.  to  balance  account, 

12 

61834 

42,1 

BUD  OE  THE  JOURNAL. 

1 

INDEX. 


291 


INDEX  TO  THE  LEGER 


A. 

ASHES,     .     .     . 

Page 
.       .       .       .      6 

Al> 
p 

Munson,  Jame^,     

age 
5 
8 
9 
3 

Ashes  in  Co.     . 
Alvardo  F.  &  Co.  my 

.     12 

ac't.  cur't.  11 

Massachusetts,  ship, 

B. 

Bills  receivable,     . 
Bills  payable      •     • 

....    2 
.     .      .      2 

N. 

Newman,  Andrew,    .... 
Nichols  &  Son,     

7 
9 

Broadcloth            . 

4 

Boots,     .... 

.     .     .     .    6 

o. 

Oil,     .     .   . 

6 

Brigham,  Joseph, 
Balance  Account, 

...     7 

.      .       .      12 

P. 

Profit  and  LOQS,     .     .     .     .     . 

3 
4 
7 

9 

e. 

Cash, 
Coffee, 
Commission, 

.      1—2 
5 

9 

Port  wine, 
Piano  Forte, 
Perkins,  Rufus,         .         .     . 

R. 

Rum,         .... 

4 

D. 

Dean,  Sam.  our  ac't 
Dean,  Sam.  ac't.  in 

.  current,  .  9 
Co.     .      .9 

S. 
Stock,     

1 

4 
5 
6 
7 

E. 

Expense  account,     .     .     .     .10 
Effingin's,Vender  his  ac't.  cur't.  11 

Samson  Lemuel,     .... 
Shoe"                 

F. 

Flour, 
Fish, 

5 

6 
...     5 

T. 

Tea,         .... 

6 
6 
7 
12 

Tow  cloth, 
Tyler,  Samuel, 
Turrel,Kingman,my  ac't.  cur't. 

G. 

...     9 

V. 

Voyage  to  Bourdeaux,     .     . 
to  Oporto,     .     . 
to  London,      .     .     . 
to  Copenhagen,     .     . 
to  New-Orleans,    .    . 
from  New-Orleans,    . 
from  Bourdeaux,    .    . 
from  Oporto,     .     .     . 
Vantorff,  Jacob,  our  ac't.  cur't. 
Vancouver  &  Sons,      .      .     . 

10 
10 
10 
10 
11 
11 
11 
12 
11 
12 

H. 

House,         ....        3 
Household  furniture,     ...      3 

L. 

.      .      .      3 

.     .     .     .    4 

Lamson,  Thomas, 

.     .     .     .     4 
.     .     .      5 

Lewis,  James,     .     . 

.      .      .     5 

Lamb,  Winslow,     . 
Lee,  Henry,  his  ac't 
Lee,  Henry,  his  ac't 
Lakeman,  Richard, 
Leroij  Chs.  my  ac't, 

.      .      .     8 

.  tobacco,  .  8 
.  current,  .  8 
.     .     .    .'  8 
current,  .  11 

w. 

Whitman,  David,     .... 
Whitman,  D.  ac't.  current,    . 
Whitman,  D.  ac't.  in  Co.     . 
Wilson,  James,    

8 
12 
12 
9 

293                                            LEGER.                                          [1 

Dr.                  Stock  Account, 

1817. 
Jan. 
Dec. 

1 
31 

J.F. 
1 

13 

To  sundries,  as  per  Journal.     .     .     . 
Balance,  for  net  stock, 

Cr. 

L.F. 

12 

$. 
4490 
61834 

C. 

42,1 

66324 

42,1 

Dr.                            Cash 

1817. 
Jan. 

Feb. 
Mar. 

April 

May 
June 

July 

Aug. 
Sept. 
Oct. 

Nov. 

1 
7 
27 
29 
31 
5 
10 
26 
7 
14 
24 
6 
20 
4 
5 
10 
18 
21 
22 
2 
3 
25 
25 
30 
18 
19 
31 
12 
27 
30 
20 
25 
30 
20 
25 
27 
28 

1 
1 
2 
2 
2 
2 
2 
3 
3 
3 
3 
4 
5 
5 
6 
6 
6 
6 
7 
7 
7 
7 
7 
7 
8 
8 
8 
8 
8 
8 
9 

9 
9 

10 
10 
10 
10 

To  Stock  on  hand, 
Rum,         .... 
Lands  in  part, 
Thomas  Lamson, 
Amos  Locke, 
Bills  Receivable,  on  J.  Thomson, 
Linen,         ... 
Bills  receivable,  A.  Young's  disco'd. 
Flour, 
Henry  Lee's  ac't.  tobacco,     .     . 
Henry  Lee's  ac't.  tobacco,      .     . 
Sundries  for  note  on  D.  Jones  &  int. 
Joseph  Brigham, 
Bills  receivable,  W.  Paterson's  note, 
Oil,         

4 
3 
4 
5 
2 
4 
2 
5 
8 
8 

7 
2 
6 
7 
4 
9 
5 
7 
8 
6 
6 
3 
3 
3 
5 
11 
6 
7 
7 
4 
4 
7 
11 
3 
8 

4000 
1215 
350 
400 
275 
350 
440 
708 
1025 
460 
194 
412 
275 
286 
250 
900 
264 
5867 
914 
495 
25 
125 
1012 
1 
3000 
2300 
1410 
1885 
578 
14 
350 
380 
2618 
870 
32203 
5054 
255 

71166 

84 

52,5 
02,8 
05 

62 

50 
48 

50 

96 

05 

75 

50 

16 
39 

35,3 

Charles  Lee, 

Samuel  Dean,  his  ac't.  current, 
Coffee,         .... 
Samuel  Tyler,  in  part, 
Robert  Means, 
Tow  cloth,         .... 

Tea,  hyson,     .... 
Profit  and  Loss, 
House  in  Hanover-street, 
Household  furniture, 
Flour,         

Voyage  from  New-Orleans, 
Tea,  in  part, 
Samuel  Tyler,  in  part, 
Samuel  Tyler,  in  part, 

Broadcloth,  in  part, 
Samuel  Tyler,  in  part, 
Voyage  from  Oporto, 
Ship  Massachusetts, 
W.  Lamb,  in  full, 

Account  transferred  to  folio  2d.    .     . 

1J                                               LEGER.                                          1Q3 

Contra,                          Cr. 

Dr. 

$.    )  C. 

1817. 

J.F. 

I..F 

Jan. 
Dec. 

1 
31 

1 

13 

By  sundries,  as  per  Journal,         .      . 
Profit  and  Loss  for  net  gain,     .     . 

3 

22527 
43796 

50 

92,1 

663-24 

42,1 

Account, 


Cr. 


1817. 

12 

1 

By  James  Lewifa, 

5 

140 

Jan. 

15 

1 

Port  wirie,         .... 

4 

336 

19 

1 

4 

901 

24 

j 

Joseph  Franklin, 

5 

1500 

24 

2 

James  Muason,         .         . 

c 

2050 

28 

2 

Lemuel  Samson, 

c 

80C 

Feb. 

2 

2 

Samuel  Tyler, 

7 

2000 

15 
20 

2 
2 

Flour,         .... 
Ship  Massachusetts, 

£ 

1925 
53 

20 

22 

2 

Broadcloth,  in  part, 

4 

875 

28 

c 
\J 

Ship  Massachusetts, 

3 

210 

75 

Mar, 

1 

0 

«J 

Henry  Lee's  ac't.  tobacco,  freight, 

8 

41 

25 

10 

2 

Henry  Lee's  ac't,  tobacco,  truckage, 

8 

11 

25 

18 

c, 

House  in  Hanover-street, 

3 

44 

37 

19 

£ 

Rum,         .... 

4 

150 

27 

4 

Henry  Lee's  ac't.  tobacco, 

8 

5 

50 

30 

4 

Henry  Lee's  ac't. 

8 

10 

50 

3] 

4 

Henry  Lee's  ac't.  current, 

8 

500 

April 

6 

4 

Expense  account, 

10 

120 

^5 

10 

4 

Voyage  to  Eourdeaux  —  Ensurance, 

10 

371 

5,7 

10 

4 

ditto,         .     .         Shipping  charges, 

10 

330 

0 

15 

5 

Richard  Lakeman, 

8 

6050 

18 

5 

Andrew  Newman, 

7 

700 

24 

5 

David  Whitman, 

8 

1562 

0 

26 

5 

Winslow  Lamb, 

8 

875 

28 

5 

Sundries,  as  per  Journal, 

1292 

0 

May 

5 

5 

Staves,         .         . 

7 

280 

8 

5 

Voyage  to  Oporto, 

10 

11 

0 

15 

6 

ditto,     for  Ensurance, 

10 

525 

5 

18 

6 

Gin,         

5 

582 

0 

June 

31 
10 
20 

6 
6 
6 

Voyage  to  London, 
Bills  payable,  to  Charles  Lee, 
Voyage  to  Copenhagen, 

10 
2 
10 

15L25 
4950 
35 

25 

7 

Voyage  to  New-Orleans, 

11 

10 

20 

July 

1 

7 

Expense  account. 

10 

119 

24 

6 

7 

Bills  payable,  to  Richard  Lakeman, 

2 

6050 

10 

7 

Bills  payable,  to  Robert  Means, 

2 

297 

85,7 

12 

7 

Thomas  Mackay, 

9 

1200 

20 

7 

Amasa  Goodhue, 

9 

10500 

I 
\ccount  transferred  to  folio  2d, 

|47433f02,4 

291,                                          LEGER.                                            [£ 

Dr.                           Cash 

Dr. 

1817. 

J.F. 

[J.F. 

$. 

C. 

To  account  brought  from  folio  1. 

71166 

35,3 

Dec. 

o 

10 

Ashes  in  Co.  with  D.  Whitman,    . 

12 

2295 

2 

10 

D.  Whitman's  acH.  current, 

12 

1020 

8 

11 

Bills  receivable,  R.  Perkins,     .  . 

2 

742 

26 

9 

11 

Port  wine,         .... 

4 

515 

12 

11 

Coffee, 

5 

947 

14 

13 

11 

James  Wilson,       .        '. 

9 

.  132 

14 

11 

A.  Ne-wman, 

7 

257 

18,4 

15 

11 

Voyage  from  Bourdeaux, 

11 

13070 

24 

1C 

11 

Piano  Fortes, 

7 

525 

18 

11 

J.  Vantorff,  our  ac't.  cur't. 

11 

14786 

48 

20 

12 

Sundries,  as  per  J. 

357 

34,4 

27 

12 

Piano  Fortes, 

7 

420 

28 

12 

Sundries,  as  per  J. 

501 

12,5 

30 

12 

Household  Furniture, 

3 

220 

30 

12 

Profit  &  Loss,  for  interest, 

3 

84 

50 

107039 

62,6 

1  Jr.                   Bills  Receivable, 

1817. 

Jan. 

1 

1 

To  Stock, 

760 

27 

2 

Lands,  on  Abram  Eastman  all  mo. 

3 

475 

Feb. 

25 

3 

Linen,  on  Alexander  "¥  oung,  a  3  mo 

4 

720 

Mar. 

4 

3 

H.Lee's  ac't.  tobacco,  for  W.P's  bill 

8 

286 

62 

24 

3 

Sugar,  on  Robert  Means,  a  9  months 

8 

1837 

50 

Dec. 

6 

11 

V.  Effingin's  ac't.  cur.  on  R.  Perkins 

11 

742 

26 

15 

11 

Voyage  f.  Bourdeaux,  J.  Henderson1* 

11 

653b 

12 

15 

11 

ditto,        T.Henshaw's  note,  a  3  mo 

11 

6535 

12 

20 

12 

R.  Means,  renewed  bill,  a  4  mo. 

8 

1837 

50 

26 

12 

Vancouver  &  Sons1  bill,  a  4  mo.     . 

12 

6975 

26704(12 

Dr.                    Bills  Payable, 

1817, 

June 

10 

6 

To  cash  paid  Charles  Lee, 

1 

4950 

July 

6 

7 

ditto          Richard  Lakeraan,     .    . 

1 

6050 

10 

7 

ditto          Robert  Means, 

1 

297 

85,7 

Aug. 

25 

8 

ditto          my  acceptance  to  H.  Lee 

,       2 

120 

Sept. 

1 

8 

ditto          to  Rufus  Perkins,     .     . 

2 

550 

Oct. 

3C 

9 

Cash,  James  Wilson, 

9 

569 

12536 

85,7 

2]                                            LECER.                                         £95 

Account,                         Cr. 

Dr. 

1817. 

J.F. 

L.F. 

$. 

C. 

Aug. 

8 

8 

By  account  brought  from  folio  1.     . 
E.  Nichols  &  Son,         .      .       . 

9 

47433 
4600 

02,4 

20 

8 

Henry  Lee,      .       .         ... 

8 

226 

79,1 

25 

8 

Bills  payable,  H.  Lee, 

2 

120 

Sept. 

1 

8 

Bills  payable,  R.  Perkins,       .     . 

2 

550 

4 

8 

Voyage  from  New-Orleans, 

11 

134 

50 

Oct. 

1 

9 

Expense  account, 

10 

127 

44 

9 

9 

V.  Effingin,  voyage  to  Amsterdam, 

11 

21 

10 

Nov. 

5 

9 

Voyage  to  London, 

10 

115 

50 

13 

10 

Voyage  to  Bourdeaux, 

11 

784 

50 

19 

10 

Voyage  from  Oporto, 

12 

1010 

40 

28 

10 

Ship  Massachusetts, 

3 

1208 

20 

Dec. 

1 

10 

Rob.  Means,       .... 

8 

2040 

3 

11 

Ashes  in  Co.  with  D.  Whitman, 

12 

86 

70 

4 

11 

D.  Whitman,  his  ac't.  in  Co. 

12 

1020 

5 

11 

S.  Dean's  ac't.  in  Co.         .     . 

9 

5867 

50 

30 

12 

Expense  account,          . 

10 

132 

40 

31 

12 

Balance  due  to  me, 

41561 

57,1 

107039162,6 

Cr. 


1817. 

Feb. 

5 

2 

By  cash,  Jacob  Thomson's  note,     .    . 

1 

350 

26 

3 

Sundries,  as  per  Journal, 

720 

April 

6 

4 

David  Jones, 

1 

410 

May 

4 

5 

William  Paterson, 

1 

286 

62 

Dec. 

8 

11 

Rufus  Perkins, 

2 

742 

26 

20 

12 

R.  Means,  bill  given  up  for  renewal, 

8 

1837 

50 

28 

12 

Abram  Eastman, 

2 

475 

31 

12 

Balance  due  to  me, 

21882 

74 

26704 

12 

Cr. 


1817. 

April 

12 

5 

By  Charles  Lee,  my  note  a  60  days, 

7 

4950 

15 

5 

Richard  Lakeman, 

8 

6050 

May 

24 

6 

Robert  Means,       .... 

8 

297 

35,7 

Aug. 

1 

8 

Rufus  Perkins,     .... 

9 

550 

15 

8 

Henry  Lee's  account  Current,     .  , 

8 

120 

Oct. 

10 

9 

James  Wilson,        .... 

9 

569 

12536 

85,7 

2CJ6                                        LEGER.                                           [3 

Dr.                   Profit  and  Loss, 

1817 
Feb. 

Dec. 

26 

14 
31 
31 

1 

J.F 
11 

12 
13 

To  bills  receivable,  for  discount  on  A 
Young's  bill,         .... 
Andrew  Newman,  for  loss  by  him, 
Expense  account,  ae  per  J.     . 
Stock,  for  m  t  gain,      .... 

Cr. 

L.F 

5 
"t 
1C 
1 

11 
4U 
49£ 
43796 

16 
61,6 
33 
92,1 

02,7 

44727 

Dr.           House  in  Hanover-street, 

itn?. 

Jan. 
Mar. 
Dec. 

1 
18 
31 

1 

3 
13 

To  Stock, 
Cash  for  repairs, 
Profit  and  Loss, 

1 

2500 

44 
455 

37 

63 

3000 

00 

Dr.             Land  in  the  County  of 

1817. 
Aug. 
Dec. 

1 
31 

1 
13 

To  Stock,        .        .        750  acres, 
Profit  and  Loss, 

562 
262 

50 
50 

825 

00 

Dr.               Ship  Massachusetts, 

1817. 
Jan. 
Feb. 

Nov. 
Dec. 

1 

1 
20 

28 
28 
31 

1 

2 
3 
10 
13 

To  Stock,         
Cash,  for  repairs, 
ditto,  for  Ensurance, 
Reimbursements  to  Europe,  cash, 
Profit  and  Loss, 

1 
1 

2 

7000 
53 
210 
1208 
3557 

20 
75 
20 
24 

1209ft 

39 

Dr.              Household  Furniture, 

1817. 
Jan. 
Dec. 
Dec. 

1 
17 
31 

1 
11 
13 

Fo  Stock,         .                           . 
Piano  Forte, 
Profit  and  Loss^ 

7 

1500 
210 
810 

2520 

LEGER. 


207 


Cr. 


Ur. 

1817. 

3.T. 

L.F. 

$. 

C. 

April 

6 

4 

By  cash,  for  interest  on  D.  Jones1  note, 

1 

2 

05 

July 

30 

7 

ditto,        ditto, 

1 

1 

96 

Dec. 

4 

Ashes,  in  Co.  with  D.  Whitman  and 

self,  my  half  of  gain, 

12 

84 

15 

in 

Voyage  to  Copenhagen  in  Co.  with 
S.  Dean  and  self,  my  half  gain, 

10 

1525 

74 

20 

12 

Cash,  for  interest, 

2 

86 

34,4 

12 

Cash  for  interest, 

2 

26 

12,5 

30 

12 

Cash  for  interest, 

2 

84 

50 

31 

13 

Sundries,  per  Journal, 

42916 

15,8 

|44727|02,7 

Cr. 


1817. 

Aug. 

10 

8 

By  cash, 

1 

3000 

3000 

Washington,                         Cr. 

1817. 
Jan. 

27 

2 

By  sundries, 

825 

825 

Cr. 

1817. 
Nov. 
Dec. 

-27 

-25 

10 

K> 

, 

12 

5054 

69^5 

12029 

39 

39 

Vancouver  and  Sons, 
i 

Cr. 

1817. 
Aug. 
Dec. 

IP 
30 

8 

12 

Cy  cash,              .              .               . 
Cash,  Piavo  Forte, 

1 

2 

2300 

220 

2.320 

__ 

LEGER. 


Dr. 


Broadcloth, 


1817. 
Jan. 
Feb. 
Dec. 

1 
22 
31 

J.F. 
1 

2 
13 

To  Stock,  a  g3,50  per  yard,    .     . 
Sundries,  a  §3,50  per  yd.     .    . 
Profit  and  Loss,         .         .     . 

Yds. 
250 
500 

Cr. 

L.T. 

$• 

875 
1750 
562 

3137 

C. 

50 
50 

750 

Dr. 


Linen, 


1817. 
-Jan. 

Bee. 

1 
18 
31 

1 
1 

13 

To  Stock,  a  ,80  per  yd. 
Andrew  Newman,  a  ,70  per  yd. 
Profit  and  Loss, 

Yds. 
400 
1000 

7 

320 
700 

520 

1540 

14CO 

Dr. 


Port  wine, 


To  Stock,  a  §45  per  hhd, 
Cash,  a  §42  per  hhd. 
Profit  and  Loss, 


Hhds 

7 
8 


15 


315 
336 
139 


790 


Dr. 


Sugar, 


J817. 

Cwt. 

Jan. 

1 

1 

To  Stock,  a  $10,50  per  cwt.     .    . 

240, 

2520 

19 

1 

Cash,  a  $10,72,6-4T  per  cwt.    . 

84 

1 

901 

Dec. 

31 

13 

Profit  and  Loss, 

54y 

yO 

324 

3970 

50 

Dr. 


Kum, 


1817. 

Gals. 

Pun. 

Jan. 

1 

1 

To  Stock,  a  $125  per  pun.    . 

12 

1500 

Mar. 

19 

3 

„    Cash,  a  $1,25  per  gallon, 

120 

1 

160 

Dec. 

31 

13 

Profit  and  Loss, 

111 

1761  1 

Dr. 


Thomas  Lamson, 


1817.1 

Jai.  I  li     llTe  Stock, 


400 


4]                                               I.EGER.                                           299 

Cr. 

1817. 
Oct. 

30 

J.F. 

9 

By  sundries,  a  $4,25  per  yd.     .     . 

Yds. 
750 

Ur. 

--I 

$. 

3187 

3187 

C. 

50 

r 

Cr. 

1817. 
Feb. 

Oct. 

10 
-25 
-25 

2 
3 
9 

By  cash,  a  §1,10  per  yd. 
Bills  receivable,  A.Youns:,  a  $1,20 
Cash,  a  ,95         .         .    "      . 

Yds. 
400 
600 
400 

1 
2 
1 

440 
720 
380 

1540 

_ 

1400 

Cr. 

1817. 
Feb. 
Dec. 

10 

9 

2 
11 

By  Joseph  Brigham,  a  g>55  per  hhd. 
Cash,  a  $51,50  per  hhd.     .     . 

Hhd?. 
5 
10 

7 
2 

275 
515 

— 

15 

790 

Cr. 

1817, 

Jan. 

Mar. 
April 

o 
20 
-20 

4 

3 
4 

By  Charles  Lee,  a  §12,50    per  cwt. 
Coffee,  a  $12  per  cwt.     . 
Robert  Means,  a  $12,  25  per  cwt. 
Robert  Means,  a  $12,50     .     . 

Cwt. 

72 
84 
150 
18 

7 
5 
8 
8 

900 
1008 
1837 

225 

50 

324 

3970 

50 

Cr. 

1817. 
Jan. 
April 
June 

7 
4 
18 
30 

1 

6 
7 
4 

By  Cash,  a  g!35  per  puncheon,    . 
"  R.  Means,  a  $1,25  per  gal.  120  gal. 
Cash,  a  $132  per  pun.     . 
James  "Wilson,  a  gl32     .  .     . 
120  gals. 

i'un. 
9 

2 
1 

12 

1 
1 
9 
8 

1215 
150 
264 
132 

1761 

of  Boston,                          Cr. 

1817.1 
Jan.  J29 

1 
2|By  Cash,         1 

400| 

300 
Dr. 


LEGER. 

Amos  Locke, 


1317. 
Jan. 


J.F. 

1 


To  Stock, 


Cr. 
r..F. 


$• 

275 


Dr. 


James  Lewis, 


1817.1     |       t 

Jan.  Il2      l|To  Cash, 


11   140| 


Dr. 


Lemuel  Samson, 


,1317.1 
Jan.  |28 

2 

To  Cash, 

t         i 

i|  cool 

Dr. 


James  Munsori, 


1817.1     I 

Jan.   |24i     2|To  Cash, 


I         I 
lU050| 


Dr. 


Joseph  Franklin, 


1317. 
Jan. 


24 1     2|To  Cash, 


l|l500[ 


Dr. 


Gin, 


1817. 

Gals. 

May 

18 

6 

To     Cash,  a  jgl,55  per  gal..     .     . 

376 

li  58280 

Pec. 

31 

13 

Profit  and  Loss     

94 

676 

:;0 

Dr. 


Coffee? 


1817. 

Ib. 

Jan 

•'0 

-• 

To  cu°"rir   a,   25  per  Ib  

4032 

4 

1000 

July 

15 

7 

Ruius  Perkins,  a  ,22  per  Ib.   .    . 

0 

550 

Dec. 

31 

13 

Profit  and  Loss,         .         .     . 



303 

62 

1861 

62 

Dr. 


Flour, 


1817.1     1 

Feb.  |15|     2iTo  Cash,  a  $8,75  per  bur. 

Dec.  31    13       Profit  and  Loss, 


111925 
510 


2435 


53. 


LEGER. 

of  Salem, 


301 
Cr. 


Dr. 

1817. 

J.T. 

L.F. 

$- 

c. 

Jan. 

33 

C) 

By  Cash,          

1 

275 

of  Boston, 


Cr. 


1817. 
Jan. 


1|     IJBy  Stock, 


140) 


of  Boston, 


Cr. 


1817.1  j 

Jan.  j   1       l|By  Stock, 


of  Boston, 


leoo! 


Cr. 


1817.1  ! 

Jan.  !  l|      l|By  Stock, 


of  Boston, 


12050! 


Cr. 


1817.)     | 

Jan.  |  Ij     l|By  Stock, 


1 1500| 


Cr. 


1817. 
Oct. 

5 

9 

By  Andrew  Newman,  a  §1,80 

-Gals. 
376 

7 

676 

80 

676 

80 

Cr. 


1817. 

Ib. 

June 

90 

7 

3^66 

i 

Q14 

At* 

Dec. 

19 

11 

ditto,  a  ,29  per  Ib  

3266 

9 

Q47 

6532 

1861 

62 

36* 


Cr. 


1817. 

iBar. 

Mar. 

? 

3 

By  cash,  a  $10,25  per  "bar.     .     .     . 

100 

1 

Aug. 

31 

8 

ditto,  a  $11,  75 

120 

1 

1410 

220 

2435 

302 
Dr. 


-LEGEil. 

Tea, 


! 

or. 

3317. 

k* 

Ib. 

L.F 

'•v 

C. 

Feb. 
Dec. 

18!     2 
3l|   13 

To  David  Whitman,  a  $1.25  per  Ib. 
Profit  and  Loss,     .... 

1250 

8 

1562 
283 

50 

75 

i 

1846 

25 

Dr. 


Ashes, 


1817. 
Aprfl 

May 

4 

20 

4 
6 

To  R.Means,a$4,04_fir  per  cwt. 
R.  Means,  a  g6  per  cwt. 

cwt.qr.lb. 
45    2   4 
49    21G 

8 

0 

225 
297 

35,7 

95    020 

522 

i).->,7 

Dr. 


Fish, 


1617.1     i 
April  1 15! 


5|To  Richard  Lakeman,  a  $3,50     .     J3400|      8r11900j 


Dr. 


Tow  cloth, 


1817.1     I 
April1  4' 


4lTo  Robert  Mean?,  a  ,2-5  per  yd. 


•Yds.]       I        , 

I  500'      81  125 


Dr. 


Oil, 


1317. 

Bar. 

1 

Apri] 

15 

5 

To  Richard  Lakeman,  a  $10     .     . 

20 

8 

2001 

Dec. 

31 

13 

Profit  and  Loss, 

501 

250| 

Dr. 


Shoes, 


1817. 
April 

28 
28 

5 

Frs. 
340 
522 

862 

1 
1 

306 
626 

932 

40 
4Q 

ditto,  a  $1,20 

i 

Dr. 


Boots, 


1817.1 


'o  cash,  o  g3  per  pur, 


IPrs.  I 

I  120'      I1  360* 


LEGKH 


303 
Cr. 


Dr. 

S-  i  c. 

1017. 

7.1'. 

Ib. 

L..F 

July 

25 

7 

By  cash  i  a  $1,50 

675 

1 

1012 

50 

Sept. 

~21 

C 

sundries,  a  $1,45 

-575 

833 

75 

1250 

1846 

25 

Cr. 


1817.1 
May  J31 


31 


jcwt.qr.lb. 
By  voya.  to  London,  a  &4,94TRT 

per  cwt.  pot,     .     .     .    I  45  2     4 


ditto,  a  §6    pearl,     .     . 


49  2  16 


225 
297 


35,7 
85,7 


Cr. 


1817.1  jQiit.l 

]VTay  I  8'      5'By  voyasre  to  Oporto,  a    3,50.    .    [34001 


Cr. 


1817.1 

July  125      7>By  cash,  a  ,25, 


ifds.j 

500!      1'  1251 


Cr. 


1817. 
June 


By  cash,  a  g  12,50  per  barrel* 


Bar. 
20 


250 


>5o| 


Cr. 


1817. 
June 


By  voyage  to  New-Orleans,  a  ,90   . 
ditto, 


Prs. 
340 

522 


862 


306  f 
626 140 

935LUO 


Cr. 


1817.1 

June  '25'    7!Bjr  yoyage  to  ^ew-Orleaas,  a 


,Prs.  j       I        i 
..  I  120'    I!'  seoi 


304»                                        LEGER.                                            £7 

Dr.                           Staves, 

1817 

May 

5 

J.F 

£ 

M. 

>  To  cash,  ft  §35  per  M.                              8 

Cr. 

L.F 
1 

sP* 

280 

C. 

Dr.                     Piano  Fortes, 

1817. 
Nov. 
Dec. 

1 
31 

9 
13 

P.  Fort. 
To  voyage  to  London,  valued,  .           6 
Profit  and  Loss,     .... 

10 

807 
347 

1155 

16 

84 

00 

Dr.                 Andrew  Newman, 

1817. 
April 
Oct. 

13 
5 

8 

To  cash,         .         .         x. 
Gin,        .         .         .         .        . 

1 

5 

700 
676 

1376 

80 
80 

Dr.                     Charles  Lee, 

1817. 
Jan. 
April 

2 
12 

l 

5 

4 
2 

900 
4950 

— 

Bills  payable,  my  note  a  CO  days, 

5850 

Dr.                    Samuel  Tyler, 

1817. 
Feb. 

2 

2 

To  cash,  lent  on  his  bond,         , 

1 

2000 
2000 



Dr.                  Joseph  Brigham, 

1817, 
Feb. 

U 

2 

4 

275 

7]                                             LEGER. 

305 
Cr. 

IS  17. 

May 

8 

I.F. 

5 

By  voyage  to  Oporto,  a  $35 

M. 
8 

Dr. 
r..p. 
10 

s.,c. 

280| 

Cr. 

1817. 
Dec. 

16 
17 

27 

11 
11 

12 

By  Cash,  a  6175. 
Homeho'ci  furniture,  a  &210 
Cash,  a  5210 

P.  Fort. 
3 
1 

cy 

o 
3 

2 

525 
210 
420 

6 

1155 

of  Portland, 

Cr. 

1817. 
Jan. 
Dec. 

18 
14 

1 
" 

4 

700 
676 

80 
80 

1376 

of  Worcester, 

Cr. 

1017. 
A  pril 
June 

10 

10 

4 
6 

By  voyage  to  Bourdeanx, 
Cash. 

• 

10 
1 

4950 
900 

— 

5350 

of  liustou, 

Cr. 

1817. 

.'ulv 
Sept. 
Oct. 
Nov. 
Dec. 

-50 

JO 

-20 

20 

7 
8 

9 
10 
12 

By  ca&h,  in  part  on  his  bond,     .... 
ditto,         ,         ditto, 
ditto,          .          ditto, 
ditto,         .         ditto, 
ditto,  in  full  of  principal,     .... 

1 
1 

1 
1 
o 

495 
14 
350 
870 
271 

2000 

of  Charleston, 

Cr. 

1817. 
April 

201    aBvca-h, 

V  275 

306                                          LEGER. 

£3 

Dr.                    Robert  Means, 

Cr. 

$• 

C. 

1817. 

J.F. 

L.P. 

Mar. 

oo 

3 

4 

1837 

50 

April 

A 

/I 

375 

May 

24 

6 

Bills  payable,  a  30  days, 

2 

297 

85,7 

Dec. 

1 

10 

Cash,  p'd  him  in  Co.  with  D.  W.  &  self, 

2 

2040 

20 

12 

Bills  rec'ble,  his  bill  given  up  for  rene. 

2 

1837 

50 

i                                                                                  6387  85,7 

Dr.                   Winslow  Lamb, 

1817. 

April 

2G 

5 

To  cash,  for  balance,         ...                1    875 

Sept. 

27 

8 

Tea,  a  60  clap,         ....           ti    255 

1                                                                                   1130 

Dr.                  David  Whitman, 

1817., 
April  [24 

5|To  cash,         .....                 1  1562 

50 

Dr.             Henry  Lee,  his  account 

1817. 

Hhds. 

Mar. 

1 

3 

To  cash,  for  freight,         .         .             15 

1 

41 

25 

1U 

3 

ditto,  for  truckage,     .     .     . 

1 

11 

25 

27 

4 

ditto,  for  weighing,      .     .     . 

1 

5 

50 

30 

4 

ditto,  for  storage, 

1 

10 

50 

JO 

4 

Commission  ac't.  for  my  com. 

9 

25 

88,2 

-JO 

4 

His  ac't.  cur't.  for  net  proceeds, 

8 

846 

79,1 

941 

17,3 

Dr. 


llichard  Lakeman, 


1817. 

April  15'     5'To  sundries,  as  per  Journal, 


Dr. 


Henry  Lee's  account 


112100! 


1817. 

Mar. 

31 

4 

To  cash,  remitted  him  by  mail,     . 

1 

500 

Aug. 

15 

8 

Bills  payable,  draft  on  myself,  in  favour 

of  C.  Lee,         .... 

2 

120 

20 

8 

Cash,  ill  full,         

2 

226 

79,1 

846 

79,1 

LEGER, 

of  Amherst, 


307 
Cr. 


jDr. 

' 

$. 

C. 

1817. 

J.T. 

L.F. 

Mar. 

24 

3 

By  bills  payable,  a  9  months,     .     .     . 

2 

1837 

50 

April 

4 

41       Sundries,         .                   .         . 

350 

May 

20 

6 

Ashes,  £larl,         .... 

6|  297 

85,7 

July 

3 

7 

Cash,         

1      25 

Nov. 

30 

10 

Ashes,  in  Co.  with  D.  Whitman  &  self, 

1212040 

Dec. 

-20 

12 

Bills  rec'ble,  his  bill  renewed,  a  4  mo. 

21837 

50 

6387 

85,7 

of  Salera, 


Cr. 


1817.1 

Feb.   22 

2 

4 

875 

Nov.  |28 

,0 

Cash, 

1 

255 

1 

11  sol 

of  Boston, 


Cr. 


1817.1 

Feb.  US'     2'Bytea. 


of  Tobacco, 


Cr. 


1817. 
Mar. 


3  By  bills  receivable,  for 
Cash, 
ditto, 


lihds. 


15 


286 '62 
460)52,5 
194  02,8 


941|17,3 


of  Ipswich, 


Cr. 


1817.1 

April  1 15'     5'By  sundries,  as  per  Journal, 


1 


'121001 


current,                          Cr. 

1817. 

Mar. 

30 

4 

By  his  ac1t.  of  tobacco,  for  net  proceeds, 

8 

846 

79,1 

; 

846 



308 
Dr. 


LrtGER. 

James  Wilson, 


Cr. 

$. 

C. 

1817. 

J.F. 

L.*. 

Jfune 

30 

7 

4 

130 

Oct. 

10 

9 

Bills  payable,  o  30  day?, 

2 

509 

701 

Dr.  Samuel  Dean,  Boston, 


1817.1 
June  20 


6  To  his  account  in  Co.  for  his  $  voyage  to 
Copenhagen,         .... 


Dr.  Samuel  Dean,  Boston, 


1817. 

Dec. 

5 

11 

To  cash,  in  part,  for  net  proceed?  on  voyage 

to  Copenhagen, 

2 

5867 

50 

31 

13 

Balance  due  to  him, 

1525 

74 

7393 

24 

Dr. 


Thomas  Mack  ay, 


1817.1 
July    12 


7  To  cash  in  full, 


1  1200 


Auiasa  troodhue, 


1817. 
July 

20 

*7 

To  cash  in  full,         .... 

1 

10500 

Dr. 


Kufus  Perkins, 


1817., 
Aug. 


8'To  bills  payable,  a  30  days, 


Dr. 


E.  Nichols  &  Sons, 


1817.1     I 
Aug.  I  8l 


8 ' To  cash  in  full, 


2'4600 


Dr. 


Commission 


1817. 

1 

Dec. 

31    13 

I 

To  Profit  and  Lo£5, 

54 

33,2 

! 

•' 

5S 

LEGER. 

of  Lynn, 


309 
Cr. 


1817. 

Oct. 

Dec. 


J.F. 

9 
11 


By  Vender  Effingin's  account  current, 
Cash,  in  full,         .... 


Dr. 

"li 

2 


569 
132 

701 


his  account  current, 


Cr. 


1817. 
June 


21 


By  Cash,  for  his  half  voyage  in  Co.  to  Co- 
penhagen,        .... 


2  5867  50 


his  acoount  in  (Jo. 


Cr. 


1817. 
June 


Dec. 


20 


18 


By  his   acH.   current,  for  his  ^  voyage  to 

Copenhagen, 
Voyage  to  Copenha.  for  his  $  share  gain, 


9  5867  50 


10 


152> 


393 


74 


24 


of  Boston, 


Cr. 


June 


20 


By  voyage  to  Copenhagen,  in  Co.  with  S. 
Dean  and  Self, 


10 


1200 


of  Newbtiryport 


Cr. 


1817. 
June 


20 


By  voyage  to  Copenhagen,   in  Co.  will 
S.  Dean,  and  Self, 


10 


10500 


of  Beverly, 


Cr. 


1317.1 
July   1 15! 


7|By  Coffee, 


!         I 
|      5[  550| 


of  Boston, 


Cr. 


1817.1 
April  [101 


4|  By  voyage  to  Bourdeaux, 


10|4600l 


Account, 


Cr. 


1817. 
Mar. 
Oct. 


By  H.  Lee's  tobacco,  my  commission, 
Vender  Effingin, 


8     2588,2 
11      2845 


I     54|33,2 


310                                         LEGER. 

Dr.                        Expense 

[10 

1817. 
April 
July 
Oct. 
Dec. 

! 

6 
1 
1 
30 

3.F. 

4 
7 
9 
12 

To  cash,  men's  wages,  &c. 
ditto,         ditto, 
ditto,         ditto, 
ditto,         ditto, 

|Cr. 

L.F 

: 

i 

c 

C 

$• 

L    120 
I    119 
>    127 
>    132 

j  499 

C. 

25 
24 
44 
40 

33 

Dr.             Voyage  to  Bourdeaux, 

1817. 
April 

Dec. 

10 
10 
31 

4 
4 
13 

To  sundries,  as  per  Journal,         .     . 
Cash,  fo*r  Ensurance, 
Profit  and  Loss,         .         .         » 

9880 
1      371 

4568 

20 
25,7 

84,3 

14820 

30 

Dr.                Voyage  to  Oporto, 

1817. 
May 

Dec. 

8 
15 
31 

5 
6 
13 

To  sundries,  as  per  Journal, 
Cash^  for  Ensurance, 
Profit  and  Loss, 

1 

12191 
525 
5580 

50 
75 

18297 

25 

Dr.                 Voyage  to  London, 

1817. 
May 
Nov. 
Dec. 

31 
5 
31 

6 
9 
13 

To  sundries,  as  per  Journal, 
Cash,  paid  at  the  C.  house,  freight,  &c. 
Profit  and  Loss,         .         » 

2j 

538 
115 
153 

807 

10,7 
50 
55,3 

16 

Dr.             Voyage  to  Copenhagen, 

1817. 
June 
Dec. 

20 
18 
18 

6 

To  sundries,  as  per  Journal, 
S.  Dean's  acH.  in  Co.  for  his  £  net  gain, 
Profit  and  Loss,  for  my  half  ditto,    . 

Rolo  Xt.T. 

9 
3 

11735 
1525 
1525 

74 
74 

14786 

48 

10J 

LEGER.                                          3£i 

Account,                         Cr. 

Dr. 

$• 

C. 

1817. 

J.F. 

L.F. 

Dec. 

31 

13 

By  Profit 

and  Loss, 

3 

499 

33 

Note.  Th 

is  account  is  balanced  by  Profit  and  Loss. 

f\e  • 

because  the 

several  things  which  are  made   Dr.   are 

of  no  value  in  a  mercantile  way,  but  an  entire  loss. 

499J33 

Consigned  to  Charles  Leroi,         Cr. 


1817. 

Nov. 

8 

<J 

By  Charles   Leroi,  my  account  current, 
for  net  proceeds, 

11 

14820 

30 

14820 

30 

Consigned  to  Francisco  Alvardo  &  Co.  Cr. 


1817. 

Oct. 

15 

9 

By  Francisco  Alvardo  &  Co.  my  account 

current,  for  net  proceeds,     .     .     . 

11 

18297 

25 

(18297 

25. 

Consigned  to  S.  Turner,  Cr. 


1817. 

Is'ov. 

1 

9 

By  S.  Turner,  my  account  current,  for  net 

proceeds,  by  the  Galen, 

7 

807 

16 

807 

16 

in  Co.  with  Samuel  Dean  and  Self,     Cr. 


1317. 

Nov. 

6 

9 

By  Jacob  VantorfT,  our  account  current, 
for  net  proceeds. 

11 

14786 

40 

14786 

48 

312                                          LEGER.                                           [U 

Dr.            Voyage  to  New-Orleans, 

1817. 
June 
Dec. 

25 
31 

J.F. 

•7 
13 

To  sundries,  as  per  Journal, 
Profit  and  Loss, 

Cr. 

L.F. 

$. 

130£ 
103 

1405 

C. 

60 
20 

80 

Dr. 


Voyage  from 


1817. 

Sept. 

3 

8 

To  Kingman  Turrel,  my  account  current. 

for  net  proceeds, 

12 

1405 

80 

Dec. 

4 
31 

8 

13 

Cash,  for  charges, 
Profit  and  Loss, 

2 

13450 

34475 

1885.|05 

Dr.     Vender  Effingin,  of  Amsterdam, 

1817. 

Oct. 
Pec. 

9 
31 

9 
13 

To  sundries,  as  per  Journal,  ^iW^Jw 
Profit  and  Loss, 

618 
123 

55 
71 

742 

26 

Dr. 


Jacob  Vantorff, 


1817. 
Nov. 


9  To  voyage  in  Co.  to  Copenhagen,  for  net 
proceeds,         .... 


14786 


Dr. 


Francisco  Alvardo  &  Co. 


1817. 
Oct. 


I  ill 

9|To  voyage  to  Oporto,  for  net  proceeds,     j    10|l829(J|25 


Dr. 


Charles  Leroi, 


1817.1 

Nov.  !  8 


|  III 

9JTo  voyage  to  Bourdeaux,  for  net  proceeds,]    10J14820J30 


Dr. 


Voyage  from 


1817. 
Nov. 


12 


1C  To  C.Leroi,  my  acH.  cur't.  for  netproc's, 
1C  Cash,  paid  at  the  Custom  house,  Sec. 
13  Profit  arid  Loss, 


11 


14820  30 
50 
10535  68 

2614t 


11]  LEGER.  ,  813 

Consigned  to  Kingman  Turrel,      Cr. 


1817. 

Aug. 


J.F. 

8 


By  K.  Turre],  my  account  current,  for  net 
proceeds,         .... 


Dr. 

$. 

C. 

1211405 
|1405 

80 
80 

New-Orleans, 


Cr. 


1817. 
.Sept. 


12 


8  By  Cash,  K.  Turrel,  for  net  proceeds, 


.885105 


1885  05 


his  Account  Current, 


Cr. 


1817. 
Dec. 


11 


By  Bills  receivable,  on  Rufus  Perkins,     .    |      2|  742  26 


r42 


•26 


our  Account  Current, 


Cr. 


1817. 
Dec. 


18 


11 


By  cash,  for  net  proceeds, 


2  14786  48 


Oporto,  my  Account  Current,        Cr. 


1817.)     | 

Nov  1  18j  10|By  voyage  from  Oporto, 


12|18297J25 


my  Account  Current,  Cr. 

1817.1     |       T~  ~~j        j  j~ 

Nov.  |12j    10!  By  voyage  from  Bourdeaux,  for  net  proc's.l    11|14820|30 


Bourdeaux, 


Cr. 


1817. 
Bee. 


15 


11 


By  sundries,    sales   at   auction,   for  net 
proceeds,        .... 


27* 


2614048 


26140 


48 


Dr. 


LEGER. 

Voyage  from 


[12 


Cr. 

$. 

C.- 

1817. 

J.F. 

L.F. 

Nov. 

18 

10 

To  Francisco  Alvardo  &  Co.  my  account 

If] 

10 

current,  for  net  proceeds,     . 
Cash,  paid  for  duties,  &c. 

11 

2 

18297 
1010 

25 
40 

Dec. 

31 

13 

Profit  and  Loss, 

12895 

51 

3-2203 

10 

Kingmau  Turret, 


18 17.  I     I 

AST.  |28j 


8 [To  voyage  to  New-Orleans,  for  net  proc's.j    I1J1405J8O 


Dr. 


David  Whitman, 


1817. 

Nov. 

30 

10 

To  his  account  in  Co.  for  his  half,  of  Ashes, 

bouefht  of  R.  Means, 

12 

1020 

Dr. 


David  Whitman's 


1317. 

Dec. 

4 

11 

To  cash,  in  part,  for  his  share  of  net  pro- 

ceeds 9n  Ashes,  in  Co. 

Q 

1020 

31 

•j<"? 

Balance  due  to  him,         .         .         . 

84 

15 

1104 

15 

Dr. 


Ashes,  in  Co.  with 


1817. 

cwt. 

Nov. 

30- 

10 

To  Robert  Means,  a  $6  per  cwt.    . 

340 

8 

2040 

Dec. 

O 
o 

11 

Cash,  paid  for  charges, 

2 

86 

70 

4 

13 

D.  Ws  ac't.  in  Co.  for  his  $  net  gain, 

12 

84 

15 

4 

13 

Profit  and  Loss,  for  my  £  net  gain, 

3 

84 

15 

Rule  XLI. 

2295 

Dr. 


Vancouver  &  Sons, 


1817. 

! 

1 

Dec. 

25 

12 

To  Ship  Massachusetts, 

3J6975J 

Dr.                  Balance  Account, 

.1817. 

• 

Dec. 

31 

13 

To  sundries,  as  per  Journal, 

63444 

31,1 

634-14 

31,1 

N.  B.  The  several  articles  under  the  head  of  Balance,  on  the  Dr, 
side,  are  brought  from  the  Cr.  side  of  that  particular  account,  which 
is  made  Cr.  u  By  Balance."  The  amount  of  these  articles  constitute 
your  net  estate  in  cash,  goods,  and  debts  due  to  you  by  others.  In 
opening  new  books,  each  of  them  must  be  made  Dr.  to  Stock,  b£™ 
cause  each  particular  is  part  of  Stock. 


12]                                            LEGER.                                         315 

Oporto,                           Cr. 

Dr. 

$.    1C. 

inn. 

T.F. 

L.F. 

Nov. 

25 

10 

By  cash,  for  port  wine,  net  proceeds,    . 

1 

32203 

16 

32203 

16 

my  Account  Current 


Cr. 


1817. 

Sept. 


31      8'By  voyaee  from  N.  Orleans,  for  net  proc'sJ    11 '1405130 


his  Account  Current, 


Cr. 


1317. 
Dec. 

2 

1C 

2 

1020 

Account  in  Co. 


Cr. 


1817. 

Nov. 

3C 

10 

By  his  account  current,   for  his   A   Ashes, 

bought  of  R.  Means, 

12 

1020 

Dec. 

4 

11 

Ashes,  in  Co.  for  his  £  share  gain,     . 

12 

84 

15 

1104 

15 

David  Whitman  and  Self, 


Ur. 


1817. 

cwt. 

Dec. 

2 

10 

By  Cash,  a  $6,75  per  cwt. 

340 

2 

2295 

22% 

— 

New-York, 


Cr. 


1817. 
Dec. 

26 

12JBy  bills  receivable,  a  4  month?.     .     .     .     |      2 

6975 

Cr. 

1817. 
Dec. 

31 

31 

13 

13 

By  Sundries,         .... 
Stock,  the  net  of  my  net  stock,    . 

1 

1609  8C 
61834  4S 

63444  31 

.  B.  The  articles  on  the  Cr.  side  of  the  balance  account,  (the  last  only  excepted,) 
»re  brc  light  from  the  Dr.  side  of  that  particular  account  which  is  Dr.  "  to  Balance.1' 
The  sum  of  these  articles  constitute  what  you  owe,  or  stand  indebted  to  others  ;  and  as 
your  Stock  is  bound  to  make  good  those  debts,  so  in  the  next  set  of  books,  Stock  must 
be  made  Dr.  to  every  one  of  them,  which  are  to  be  considered  as  so  many  creditors  to 
whom  you  are  indebted.  The  last  article  only,  where  Balance  is  made  Cr.  by  Stock, 
exhibits  the  net  of  your  whole  estate,  and  what  you  are  worth  after  your  debts  are  paid. 
This  balance  is  entered  on  the  Cr.  side,  (except  where  the  debts  exceed,)  and  in  your 
next  set  of  books,  Stock  must  be  credited  with  the  same,  for  the  whole  quantity  and 
value,  because  each  particular  is  Dr.  to  Stock  for  its  respective  quantity  and  value.  If 
what  you  owe  should  exceed  your  cash,  goods  unsold,  and  debts  due  to  you,  the  balance 
must  be  placed  on  the  Dr.  side,  and  shows  how  much  you  are  worse  than  nothing1 :  Thi» 
evil  may  happen  by  unavoidable  misfortunes  and  losses,  but  will  seldom  be  the  case  ' 


GENERAL  TRIAL  BALANCE. 

1234 


Titles  of  Accounts. 

LF 

Dr. 

$. 

C. 

Cr. 
f. 

c. 

Balance. 
Dr.  $|  C. 

Cr. 
$. 

C. 

Stock,  

1 

2 

2 
3 
3 
3 
3 
3 
4 
4 
4 
4 
4 
5 
5 
5 
6 
6 
7 
9 
9 
10 
10 
10 
10 

11 
11 
11 
11 

12 
12 

4490 
107039 
26704 
430 
2544 
562 
8472 
1710 
2625 
1020 
651 
3421 
1650 
582 
1558 
1925 
1562 
200 
807 
5867 

62,6 
12 
77,6 
37 
50 
15 

22527 
65478 
4821 
1810 
3000 
825 
12029 
2520 
3187 
1540 
790 
3970 
1761 
676 
1861 
2435 
1846 
250 
1155 
7393 
54 

50 
05,5 
38 
86,9 


41561 
21882 

499 

57,1 

74 

33 

18037 

1380 
455 
262 
3557 
810 
562 
520 
139 
549 
111 
94 
303 
510 
283 
50 
347 
1525 
54 

4568 
5580 
153 
103 
344 
123 
10535 
12895 
84 

50 

09,3 
63 
50 

24 

50 
50 

62 
75 

84 
74 
33,2 

84,3 

55,3 
2Q 
75 
71 
68 
51 
15 

Cash,  

Bills  Receivable,  . 
Profit  and  Loss,  .  . 
House  in  Hanover-st 
Land,  
Ship  Massachusetts, 
HouseholdFurniture 
Broadcloth,  .... 

39 

50 

Port  wine,  .... 
Su£3.r 

80 
50 

50 

80 

S2 

Flour,  

Tea,  . 

25 

Oil,  

Piano  Fortes,  .  .  . 
S.Dean^sacH.inCo. 
Commission,  .  .  . 
Expense  ac't.  .  .  . 
Voya.  to  Bourdeaux, 
Oporto,  . 
London,  . 
N.  Orleans, 
Voya.  fr.  N.  Orleans, 
Vender  Effingin,  .  . 
Voya.  fr.  Bourdeaux, 
Oporto,  .  . 
D.  Whit's  ac't.  inCo. 

Proof,    .... 

16 
50 

24 
33,2 

489 
10251 
12717 
653 
1302 
1540 
618 
15604 
19307 
1063 

33 

45,7 
25 
60,7 
60 
30 
55 
80 
65 
35 

14820 
18297 
807 
1405 
1885 
742 
26140 
32203 
1147 

30 
25 
16 
80 
05 
26 
48 
16 
50 

63943 

164,1 

63943 

64,1 

MONTHLY  TRIAL  BALANCE, 


1817. 

Dr.  $. 

C. 

Cr.  $. 

C. 

January   31 

38067 

50 

38067 

50 

February  28 

10006 

45 

10006 

45 

March    31 

7276 

71,6 

7276 

71,« 

April     30 

45363 

35,7 

45363 

65,7 

May     31 

15000 

49,1 

15000 

49,1 

June     30 

32183 

08 

32183 

08 

July     31 

20376 

55,7 

20376 

55,7 

August   31 

13732 

59,1 

1373? 

59,1 

September  30 

4823 

10 

4823 

10 

October   31 

24206 

54 

24206 

54 

November  30 

115485 

88 

115485 

88 

December  31 

80477 

61,9 

80477 

61,9 

Proof,  .  . 

407000 

18,  i 

407000 

18,t 

PROFIT  AND  LOSS  SHEET. 


13  r.                  Profit  and  Loss,                  Cr. 

TITLES. 

Expense  account, 
In  Leger,  page 

To  Stock,  for  net 
gain,     .     . 

L.F. 

10 
£ 

3 

$• 
499 
430 

C. 

33 

77,6 

TITLES. 
House  in  Han.-st. 
Lands, 
Ship  MassachusHs. 
Household  furni. 
Broadcloth,  .  .  . 

L.F. 

3 
3 
3 
3 
4 
4 
4 
4 
4 
5 
5 
5 
6 
6 
7 
9 
10 
10 
10 
11 
11 
11 
11 
12 

3 

$• 

455 
262 
3557 
810 
562 
520 
139 
549 
111 
94 
303 
510 
283 
50 
347 
54 
4568 
5580 
153 
103 
344 
123 
10535 
12895 

C. 

63 
50 
24 

50 

50 

62 
75 

84 
33,2 
84,3 

55,3 
20 
75 
71 
68 
51 

93G 
43796 

10,6 
92,1 

Port  wine,    .    .  . 
Sugar,     .     .      . 
Rum,    .... 
Gin,     .... 
Coffee,     .     .     . 
Flour,     .     .     . 
Tea,     .... 

Oil,     .... 
Piano  Fortes,  .  . 
Commission,  .   . 
Voya.  to  Bourd'x. 
Oporto, 

N.Orleans 
fr.  N.Orleans 
Vender  Effingin, 
Voya.  fr.  Bourd'x. 
Oporto, 

In  Leger,  page 

42916 
1810 

15,8 
86,9 

4,4727 

02,7 

44727 

02,7 

BALANCE  SHEET. 

Dr.                  Balance  Account,                 Cr. 

To  Cash,  .  . 
Bills  receivable, 

2 

2 

41561 
21682 

57,1 
74 

By  Samuel  Dean's 
ac't.  in  Co.   . 
D.  Whitman's,  do. 
Stock,  net  of  my 
estate,     .     . 

9 
12 

1 

1525 
84 

61834 

74 
15 

42,1 

63444(31,1 

63444131,1 

APPENDIX. 


THE  following  concise  description  of  the  secondary  or  auxilif 
books  will  suffice  to  give  the  young  book-keeper  an  idea  of  their  for 
and  use. 

1.  Cash  Book. 

The  use  of  this  book  is  to  shorten  the  cash  account  in  the  Leger, 
to  which  is  transferred  the  account  of  cash  received  and  paid  out 
each  month.  Instead  of  this  book,  some  merchants  open  a  "  cash 
account,"  in  the  Leger.  By  the  cash  book  the  merchant  can  at  any 
time  ascertain  the  exact  sum  of  money  on  hand,  without  the  trouble 
of  telling  it  over.  For  its  form,  see  Cash  Account,  Leger  p.  1  &  2« 

2.  Bill  Book. 

The  merchant  by  this  book  is  enabled  to  ascertain  the  time,  when. 
•jills  or  other  debts  become  due  payable  to  or  by  him.  It  consists  of 
a  folium  for  each  month.  The  sums  to  be  received  are  entered  on 
the  left  hand  page,  and  those  to  be  paid  on  the  right  hand.  Bills 
receivable  are  those  which  the  merchant  receives  in  payment  of  some 
debt  or  contract,  and  bills  payable  are  such  as  are  drawn  upon  him, 
and  which  he  must  pay  when  due.  For  the  form  of  the  book  and 
bill,  draft  or  note  of  hand,  see  Appendix,  Nos.  I.  II.  IX. 

3.  Invoice  Book. 

An  invoice  is  a  paper  sent  off  with  goods  exported,  either  for  the 
merchant's  account  or  for  others.  It  is  headed  generally  with  the 
name  of  the  ship,  master,  place  whtre  bound,  and  of  the  person  to 
whom  the  consignment  is  made.  This  book,  containing  the  copies 
of  invoices  sent  off,  is  sometimes  called  the  invoice  outward,  to  dis- 
tinguish it  from  the  invoice  inward,  which  contains  the  copies  of  in- 
voices received  from  abroad.  For  the  form  of  invoice,  see  Appendix 
NoV. 

4.  Sales  Book. 

This  book  is  used  to  trace  the  net  proceeds  of  any  cargo,  or  con- 
signment sold  on  commission.  It  exhibits  each  consignment  separate 
and  by  itself,  to  which  are  subjoined  the  respective  charges,  such  as 
freight,  custom,  truckage  and  commission,  &c.  The  amount  of  these 
subtracted  from  the  gross  amount  of  sales  shows  the  net  proceeds  ; 
for  which  the  factor  gives  his  correspondent  credit,  and  sends  him  a 
copy  of  the  account  sales,  signing  to  it  his  name,  with  the  words 
"•  Errors  Exempted."  From  this  book,  when  a  consignment  is  sold 
off,  an  account  is  drawn  out,  to  be  transmitted  to  the  employer. 
For  form  of  an  "^Account  Sales,"  see  Appendix  No.  VI. 

5.  Account  Current  Book.      « 

This  book  contains  the  copies  of  such  accounts  as  are  sent  to  cor- 
respondents. Although  they  have  the  form  of  the  Leger,  yet  they 
are  more  particular  than  the  general  entries  of  it ;  for  the  charges, 
which  are  collected  into  one  sum  in  the  Leger,  mayjn  the  Journal 
post  have  several  lines;  therefore  an  exact  copy  is  necessary  to  pre- 
vent disputes.  The  accounts  should  exactly  correspond  with  the 
Leger,  omitting  the  terms,  "  Sundries,*  "  JVWe*  payable,"  " 


APPENDIX. 

receivable,"  Expense  account,"  &c. ;  by  which  the  Leger  account  has 
been  either  debited  or  credited.  For  the  form  of  an  Account  Cur- 
rent, see  Appendix  No.  VII. 

6.  Commission  Book. 

This  book  contains  a  fair  copy  of  all  orders  received  from  corres- 
pondents, by  which  the  merchant  should  carefully  regulate  his  con- 
duct in  transacting  business  for  others,  that  he  may  avoid  all  losses 
arising  from  mistakes  committed  by  himself. 

7.  Book  of  Ship's  Account. 

This,  like  the  invoice  book,  contains  too  many  particulars  to  be 
left  to  the  entry  of  the  Waste-book.  All  the  expenses,  from  the  ar- 
rival to  the  sailing  of  the  ship,  should  make  but  one  entry. 

8.  Expense  Account  Book. 

It  contains  the  daily  expenditures,  such  as  men^  wages  and  other 
incidental  charges.  The  prudent  merchant  will  ever  feel  anxious  to 
know  the  amount  of  his  contingent  expenses,  the  better  to  ascertain 
the  exact  state  of  his  income.  Its  form  is  similar  to  u  Cask  account.'''' 

9.  Letter  Book. 

The  bad  consequences  which  often  attend  the  neglect  of  preserv- 
ing an  exact  copy  of  letters  sent  on  business,  have  induced  the  care- 
iul,  regular  merchant,  to  copy,  verbatim,  all  such  letters  into  a  large 
folio  volume,  allotted  for  that  purpose.  So  that  this  book,  with  the 
letters  received,  which  should  be  carefully  kept  in  files,  mzJie  a  com- 
plete history  of  the  mercantile  transactions  betwixt  the  merchant  and 
his  correspondent. 

When  an  answer  is  received,  mention  at  the  end  of  the  foregoing 
letter,  the  date  of  that,  which  came  for  answer. 

When  an  answer  is  returned  to  any  letter  received,  note  on  the 
letter  the  time  of  answering  it. 

10.  Postage  Book. 

It  contains  all  the  letters,  which  the  merchant  receives,  and  sends 
away  on  account  of  his  correspondent,  for  which  he  pays  postage. 
The  sum  total  is  carried  to  the  account  current. 

1 1 .  Receipt  Book. 

This  book  contains  the  receipts  which  a  merchant  takes  for  the 
payments  he  makes.  The  receipt  should  mention  the  date,  sum  re- 
ceived, expressed  in  words  at  large,  and  in  figures  in  the  money 
columns ;  the  reason,  whether  in  full  or  in  part,  and  must  be  signed 
by  the  person  receiving.  For  the  form  of  Receipts,  See  Ap.  No.  VIII. 

12.  Check  Book. 

The  form  of  the  check -book  is  various,  but,  perhaps,  equally  con- 
venient. It  is  Ijke  the  cash  book,  and  may  be  kept  by  debit  and 
credit.  For  form,  see  No.  X. 

The  memorandum,  or  pocket  book,  is  kept  by  factors  in  extensive 

business.     In  it  is  copied,  from  letters  received,   short  notes  of  the 

several  commissions  for  buying  goods,  contained  in  them.     It  greatly 

facilitates  the  mode  of  doing  business,  by  assisting  the  memory  with- 

i   continuaj  reference  tp  the  letters  themselves. 


APPENDIX. 


The  preceding  are  the  auxiliary  books  commonly  used  by  different 
merchants,  who  are  not,  however,  restricted  in  the  use  of  them  ;  but 
adopt  such  of  them  only  as  are  most  convenient  to  them,  according 
to  the  nature  and  extent  of  their  business. 


MERCANTILE  FORMS. 

No.  I.     BILL  BOOK. 


Bills  receivable,  January,  1817. 


J.F. 

When 
receiv- 
ed. 

From 
whom     re- 
ceived. 

By  whom 
drawn,  and 
place. 

On  whom 
drawn,  and 
place. 

Date. 

To  whom 
payable. 

Time. 

Due. 

Dec. 
6 

Sum. 

Dec.  5 

V.Effing-in. 

W.  Vorst, 

Amsterdam. 

R.Perkins, 
Boston.    . 

Nov. 
9 

Th.  Rus- 
pell. 

At 
sijfht. 

D.    0. 

742,<26 

No.  II. 

Bills  payable,  January.  1817. 


J.F. 

By  whom  drawn, 
and  place. 

Date. 

To  whom 
payable. 

Time. 

Accepted 

Due. 

An:;. 
27 

Sura. 

To  whom  p'd. 
and  when. 

Charles   Lee, 

Aii£.  25. 

Henrv  Lee, 
Norfolk. 

July 

v3 

C.  Lee. 

10  days 
after  sight. 

Aug.  15 

P. 
120 

No.  III.     FOREIGN  BILL 

Form  of  a  bill  of  exchange  received  from  Vender  Effingin  of  Am- 
sterdam, and  entered  in  bills  receivable,  as  in  No.  I. 
Gilders.  Stivers. 

1855       13    a  40  c. 

Amsterdam,  Nov.  1,  1C17. 

Thirty  days  after  sight,  pay  this  my  first  bill  of  exchange,  (my 
second  and  third  of  the  same  tenor  and  date  not  paid)  to  Thomas 
Russell,  or  order,  one  thousand  eight  hundred  and  fifty-five  gilders 
thirteen  stivers,  exchange  40  c.  per  gilder,  for  value  received,  and 
place  the  same  to  acconnt,  per  advice  from  WILLIAM  VORST. 

To  Rufus  Perkins,  Boston. 

Accepted,  December  6,  1817.  RUFUS  PERKINS. 

No.  IV.    INLAND  BILL. 

Form  of  a  bill  drawn  on  rno  by  Hrnry  Lee,  and  entered  in  bills  pay- 
able, as  in  No.  II. 
$120 

Norfolk,  (Virginia.)  July  28,  1817. 

Ten  da}*s  after  sight,  pay  to  Mr.  Charles  Lee,  or  order,  one  hun- 
dred and  twenty  dollars,  for  value  received,  and  place  it,  without 
further  advice,  to  the  account  of  your  humble  servant, 

HENRY  LEE. 
To  Thomas  Russell,  Boston. 

Accepted,  August  15,  1817.  THOMAS  RUSSELL. 

N.  B.  A  bill  of  exchange  is  a  written  order  for  money,  to  be  re- 
ceived in  one  place  or  country,  for  value  paid  in  another.  Their 
style  varies  according  as  one  or  more  bills  are  drawn  for  the  same 
sum ;  or  according  to  the  time  of  payment,  as,  at  sight,  so  long  after 
sight,  at  usance,  or  double  usah.ce,  &c. 


APPENDIX. 


321 


No.  V. 

Invoice  of  10  hhds.  tobacco,  shipped  on  board  the  Mary-Ann,  Capt. 
Hoffman,  for  Amsterdam,  by  order  of  Vender  Effingin,  merchant 
there,  for  his  account  and  risk,  and  to  him  consigned. 

Boston,  Oct.  9,  1817. 


V.E. 

No.    1  gross  1340  Ib. 

tare  84  Ib. 

$. 

C. 

No. 

2 

1574 

90 

ItolO 

3 

1394 

89     14225  Ib.  a  $4  per  100  Ib. 

569 

4 

1504 

96                Charges. 

5 

1479 

88     Shipping  charges,  $21,10 

6 

1584 

87     Commis'n,  a  5  p.  c.  28,45 

7 

1498 

90                                  

49 

55 

8 

1640 

100 





9 

1549 

99 

618 

55 

10 

1584 

98 

___ 





Errors  excepted. 

Gross, 

15146  tare,  921            Boston,  Oct.  9,  1817. 

Tare, 

921 

Net, 

14225  Ib. 

Bought  of  James  Wilson, 

a  30  days,  $569. 

JSo.  VI. 

?ales  of  15  hhds.  tobacco,  received  per  brig  Favorite,  and  sold  by 
order,  and  for  account  and  risk  of  Henry  Lee,  of  Norfolk,  (Vir.) 


1817 

Dr. 

1817. 

Cr. 

Mar. 

1 

To     cash,    paic 
freight,  15  hhds. 

$• 

C. 

Mar. 

' 

By  W.  Paterson's  bill,  a 
90  days,  for  4  hhds. 
Ib.       Ib. 

$• 

C. 

fr.  Norfolk,  re- 

No. 1  gross,  103  14  ta.  145 

ceived   per  brig 
Favorite,  .  .  . 

41 

25 

2             11  2  17       150 
3               9  3  24       135 
4             10  0  27       140 

1  r 

Cash   p'd  truck- 

27 

age,  .... 
Cash,  p'd  weigh- 
ing, &c.  .  .  . 

11 

c 

25 
50 

14 

42  2  25       570 
Makes  4215  Ib.    net, 
a  D.6,80per  100  Ib.    . 
By  cash,  8  hhds. 

283 

62 

30 

Cash,  Storage, 
Commission,  a  5 

10 

50 

Ib.      Ib. 
N"o.  5  gross    8  2  13  ta.  13o 
6              91              140 

I 

per  cent.  .  . 

25 

88,2 

7            10014        138 

Henry  Lee,   for 
net  proceeds, 

846 

79,1 

8              8  3  15        145 
9              7  3  23        125 
10              9  1  13        132 

11            10014        140 

12               8  2  14         130 

72  3  22      1035 

Is  7085  Ib.  net,  a  D.6,50 

per  100  Ib. 

24 

By  cash,  3  hhds. 

460 

52,5 

Ib.       Ib. 

Errors  excepted. 

\o.  13  gross    92  12  ta.  146 

14              83  27        133 

Boston, 

15             10  1  13        148 

March  30,  1817. 

23  3  24      43  J 

. 



s  2812  Ib.   net,  a  D.  6,90 

94 

02,6 

341 

17,3 

per  100  Ib.      .      .      . 

41 

7,8 

APPENDIX. 


No.  VII.    AN  ACCOUNT  CURRENT. 

Dr.  Henry  Lee,  of  Norfolk,  in  account  with  Thomas  Russell,  Cr. 


1017. 

$. 

C. 

1817. 

Mar. 

31 

To  cash,   remit- 

Mar. 

30 

By  net  proceeds 

ted  by  the  mail, 

500 

of  15  hhds.  to- 

Aug. 

15 

Your  draft,  in  fa- 

bacco,   as    per 

vor  of  C.  Lee, 

120 

acH.  sales  ren- 

20 

Cash,forbalance 

226 

79,1 

dered,  .... 

846 

79,1 

Errors  excepted. 

Boston, 





.  — 

—  —  . 

Aug.  20,  1817. 

846 

79,1. 

846 

79,1 

J\"ote  for  t?ie  pupil.  When  a  person  or  dealer  not  only  buys  from  the  merchant,  but 
sells  to  him,  or  transacts  business  for  him,  so  as  to  render  the  merchant  Dr.  to  him,  the- 
uccouut,  in  this  case,  is  denominated  by  nu'rr.hants  "  Ait  Account  Cm  rent." 

No.  VIII.     FORM  OF  JIN  ACCOUNT  SALES. 

Sales  of  15  hhds.  tobacco,  received  per  brig  Favorite,  C.  Hunt,  sold 
by  order,  for  account  and  risk  of  Henry  Lee,  Norfolk. 

1817. 
Mar. 


4 
14 

! 
j 

j 

1 

To  W.  Paterson's  bill  a  90  days,  for  4  hhds. 
No.  1  gross  10  3  14  Ib.  tare  145  Ib. 
2           11  2  16                 150 
3              9  3  24                 135 
4            10  0  27                 140 

286 

460 

194 

94 
846 

62 

52,5 

02,8 

38,2 
79,1 

42  2  25                  570 

Net  4215  Ib.  a  $6,80  per  100  Ib,    .    . 

To  cash,  8  hhds. 
No.  5  gross    8  2  13  Ib.  tare  135  Ib. 
691                       140 
7           10  0  14                138 
8              8  3  15                 145 
9              7  3  23                 125 
10             9  1  13                132 
11            10  0  14                 140 
12             8  2  14                 130 

72  3  22               1085 

Net  7085  Ib.  a  $6,50  per  100  Ib.    .    .. 

To  cash,  tor  3  hhds. 
No.  13  gross    9213  Ib.  tare  146  Ib. 
14             8  3  27                 138 
15           10  1   13                148 
28  3  24                 432 
Net  28fHb~a  $6,90  per  100  Ib.     .    . 
Charges. 
Freight,        ...                    .          $41,25 

Weighing  and  truckage,         .         .         ,       16,75 
Storage                   10,50 

Commission,  on  $941,17,3  a  2|  per  cent.     25,88,2 

j  Bostpn,  March  24,  1817.         Thomas  Jtoell 

323 

No.  IX.     RECEIPTS. 

1.  A  General  Receipt. 

Boston,  April  14,  1818.     Received  from  Thomas  Lamson,  four 
hundred  dollars,  in  full  of  all  demands, 

SAMUEL  SAWYER. 
$400 


N.  B.  A  general  receipt  will  not  discharge  debts  due  on  bonds, 
bills  and  other  instruments  executed  by  scaling  and  delivering  ;  nor 
•will  it  discharge  negotiable  notes,  or  inland  bills. 

2.  Receipt  for  money  received  on  Note. 

Boston,  April  14,  1818.  Received  from  James  Snow,  by  William 
Spooner,  four  hundred  and  ninety-five  dollars,  which  is  endorsed  on 
liis  note  of  January  4,  1818. 

LEMUEL  VOSE. 

$495 

3.  Receipt  for  money  received  on  Account. 

Boston,  April  14,  1818.  Received  from  Andrew  Bond,  fifty 
dollars,  on  account. 

WILLIAM  SIMSON. 

$50 

4.  Receipt  for  money  received  for  another. 
Boston,  April  14,  1818.     Received  from  James  Wilson,  one  hun- 
dred and  fifty  dollars,  for  account  of  Thomas  Newman. 

For  Thomas  Newman, 
$150  GIDEON  RICE. 

No.  X.    PROMISSORY  NOTES. 

1 .  Jl  note  on  demand. 

Boston,  April  15,  1818.  For  value  received,  I  promise  to  pay 
Mr.  James  Scott,  or  order,  one  thousand  dollars,  with  interest,  on 
^demand. 

BENJAMIN  KURD. 

$1000 

Attest,  Jacob  Ingraham. 

N.  B.  1.  Notes  of  hand,  draughts  or  orders,  and  acceptances,  are 
entered  in  the  accounts  of  bills  receivable  and  payable. 

2.  A  promissory  note  draws  interest  from  the  date  to  the  pay- 
ment, unless  otherwise  expressed  in  the  note. 

3.  A  note  or  bill  is  not  endorsable,  and  consequently  not  negotia- 
ble, unless  it  is  payable  "  to  order  ;"    nor  is  it  valid,  unless  it  ex- 
presses, "  for  value  received." 

2.  Jl  note  by  two  persons. 

Boston,  April  15,  1818.  For  value  received,  we,  jointly  and  sev- 
erally, promise  Mr.  Abram  Foster,  to  pay  him,  or  order,  one  hun- 
dred dollars  in  three  mouths,  with  interest  after. 

AMOS  HILL, 
THOMAS  SHAW. 
Attest,  Stephen  Mo«dj< 


324 


APPENDIX, 


3.  Note  for  borroived  money. 

Boston,  April  15,   1818.      Borrowed   and   received  of  Jonathan 
Whiting,  thirty  dollars,  which  I  promise  to  pay  on  demand. 

JAMES  TRUSTY, 
No.  XI. 
Check  Book. 


Dr.  New-England  Bank,  in  account  with  John  Grant,  Cr. 


1817.1 

$• 

1817. 

$. 

0. 

Jan. 

12 

To  Cash,  .  .    . 

1450 

Jan. 

16 

By  Cash,  J.  Stim. 

750 

18 

ditto,  .... 

920 

20 

Wm.  Sumner, 

435 

24 

Bill,  S.  Miles, 

790 

•r 

23 

S.  Hunter,  . 

1000 

25 

Cash,     .     . 

1005^ 

28 

Cash,toW.V. 

250 

30 

Cash,    .    .    . 

434 

29 

William  Hunt, 

167 

31 

Cash,  to  A.  R. 

460 

Balance,  .    . 

1537 

4599 

4599 

N.  B.  When  a  note  of  hand  is  offered  at  the  Bank  for  discount 
two  endorsers  are  commonly  required,  the  note  being  made  payable 
to  the  first.  The  form  is  as  follows, 

Boston,  April  15,  1818.  For  value  received,  I  promise  to  pay  one 
hundred  and  fifty-five  dollars,  to  Thomas  Smith,  or  order,  at  the 
Union  Bank,  in  fifty-seven  days,  with  grace.* 

ANDREW  MEANS. 

$155 

*  Grace  means  a  t«rm  of  three  days  given  to  the  borrower,  that  is, 
the  borrower  may  withhold  the  payment  until  sixty  days  have  ex- 
pired, because  the  interest  is  computed  for  sixty  days,  notwithstand- 
ing the  note  should  be  paid  the  fifty-seventh  day. 

2.  For  the  method  of  discounting  notes,  see  Bank  Discount 
— Pract.  Arith.  p.  153. 

The  discount  on  notes  is  the  interest  of  the  sum  from  the  date  of 
i.he  note  to  the  time  it  becomes  due,  including  the  days  of  grace. 
This  interest  is  deducted  from  the  amount  of  the  note,  before  the 
borrower  receives  his  money^  and  therefore  may  take  the  benefit  of 
the  days  of  grace. 

No.  XII.    AN  ORDER. 

Boston,  April  17,  1818. 

Sir,. 

Please  to  pay  to  Mr.  Thomas  Dwight,  or  order,  four  hundred 
dollars,  and  this  shall  be  my  receipt  for  the  same. 

WILLIAM  VASSAL, 
Mr.  Horatio  Gates. 

No.  XIII.    ^JV  ORDER  FOR  GOODS. 

Boston, -Sept.  18,  1818. 
Sir, 

Please  to  deliver  Mr.  John  Goodhue,  such  goods  as  he  may  call 
for,  not  exceeding  the  sum  of  three  hundred  dollars,  and  charge  the 
same  to  the  account  of  your  humble  servant, 

AARON  DEXTER. 
Mr,  Robert  Munson, 


YA  02432 


